GMAT practice probs 2
fuel economy is E km/L when driving speed at constant S km/hr. In terms of S and E, what reps # liters of fuel used in 1 hour of driving under ideal at S and number of liters of fuel used in 60 km drive at speed S?
1 hour: S/E 60 km: 60/E
If T is a list of consecutive integers in increasing order, what is the sum of integers in T? (1) The difference between the last integer in T and the first integer in T is 100. (2) The fourth integer in T is -6
1) The difference between any two integer is 100.So,Let first number could be -1,0,or,1 then last number would be 99,100,or 101 and each series give different sum. Hence, Not Sufficient. 2) fourth integer is -6 .so first integer is n+3=-6 i.e -9 but we don't know the number of of terms in T. that sum of 100 terms of sum of 200 terms. Not sufficient 1) and 2) together we know that first integer is -9 and difference of last integer and first integer is 100. So we definitely get a sum.Hence C is the correct answer
if r and s are positive integers, is r/s an integer? 1) every factor of s is also a factor of r 2) every prime factor of s is also a prime factor of r
1. SUFF the integer s is by definition a factor of itself. from this, every factor of s is also a factor of r. so r/s must be an integer 2. insuff. if r= 18, s=6 then 6 has the prime factors 2 and 3 each of which is also a factor of 18, and r/s=18/6 is an inte.t but if r = 18 and s= 8, then r has the primary factors 2 and 3, and s has a prime factor 2, which satisfies this condition. r/s = 18/8 not integer. A
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. A. 100 B. 140 C. 150 D. 160 E. 200
38 = .1*x + .15*(300-x) .05x = 7 x= 140
1/ (1 + 1/(2+1/3) =
7/10
In 1992 outlaw fishing boats began illegally harvesting lobsters from the territorial waters of the country of Belukia. Soon after, the annual tonnage of lobster legally harvested in Belukian waters began declining; in 1996, despite there being no reduction in the level of legal lobster fishing activity, the local catch was 9,000 tons below pre-1992 levels. It is therefore highly likely that the outlaw fishing boats harvested about 9,000 tons of lobster illegally that year. Which of the following is an assumption on which the argument depends? A. The illegal lobster harvesting was not so extensive that the population of catchable lobsters in Belukia's territorial waters had sharply declined by 1996. B. The average annual lobster catch, in tons, of an outlaw fishing boat has increased steadily since 1992. C. Outlaw fishing boats do not, as a group, harvest more lobsters than do licensed lobster-fishing boats. D. The annual legal lobster harvest in Belukia in 1996 was not significantly less than 9,000 tons. E. A significant proportion of Belukia's operators of licensed lobster-fishing boats went out of business between 1992 and 1996.
A Premise: illegal lobster harvesting began in 1992. Premise: legal catch was 9k tons below pre-1992 levels. Conclusion: it is highly likely that illegal harvest was about 9k tons. A defends the conclusion by eliminating the possibility that lobster population may have decreased because of rampant harvesting since assumption strengthens the conclusion .. its logical negative should weaken the conclusion logical negative of A: illegal harvest was so extensive that lobster population sharply declined. the logical negative clearly weakens the conclusion .. and passes the test A is correct
In order to conserve the energy and heat they need to spend the entire winter sitting motionless over incubating eggs, male emperor penguins huddle over the nests in groups, *thereby reducing the rate at which they burn energy so that it is 25 percent lower than it would be for* isolated birds. A)thereby reducing the rate at which they burn energy so that it is 25 percent lower than it would be for B)thereby reducing their rate of burning energy until it is 25 percent lower when compared with C)and they thereby reduce by 25 percent the rate they burn energy, as compared to what it would be with D)which thereby reduces by 25 percent their rate of burning energy, when comparing them to E)which thereby reduces the rate they burn energy so that it is 25 percent lower than
A.
Letter to the editor: Our city plans to allow major commercial development along the south waterfront and, in so doing, to increase its tax revenue. But, to succeed commercially, the development would inevitably create far more road traffic than the existing roads to the waterfront can handle, causing serious traffic congestion. Providing enough roads or public transportation to the area would cost far more than the city could gain from the increased tax revenue. Which of the following, if added to the city's plan, would be most likely to help solve the problem the letter describes? (A) Funding construction of new roads to the waterfront with a system of tolls on the new roads to the waterfront (B) Allowing residential development along the waterfront so that there will be waterfront residents who can walk to the commercial development (C) giving tax breaks to developers of businesses along the waterfront to offset any tax levied on them for construction of roads or public recreation (D) Evaluating the net benefits that the commercial development would bring to the city in terms of improved quality of life for the city's residents rather than its financial terms (E) Allowing commercial development in other city neighborhoods whose roads are not seriously congested with traffic
A. (A) Funding construction of new roads to the waterfront with a system of tolls on the new roads to the waterfront Toll roads! That magic form of income! Yes, this would have the advantage that more traffic leads to more money, so as long as traffic is a problem, there's money coming in that can solve the problem. Brilliant! This works as a correct answer. (B) Allowing residential development along the waterfront so that there will be waterfront residents who can walk to the commercial development Hmmm. Not satisfying. Those residents would still have to drive home and park, adding to traffic, and folks who live elsewhere would still have to drive there. It doesn't sound as if this would do much to solve the problem. This is incorrect.
If p is an integer greater than 1, is p a prime number? (1) p is a factor of 13 (2) p is a factor of 78
A. 1) SUFF must be 13 or 1, but p > 1, so it's 13. 2) INSUFF p could be prime since 2 is a factor and is prime but it could also be composite since 6 is a factor and is composite.
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 8 III. 11 (A) ΙI only (B) ΙII only (C) I and ΙI only (D) II and ΙII only (E) I, ΙΙ, and ΙΙI
A. 8 = 3 + 5 --> cannot be a triangle. leg must be LESS than the sum of the other 2 sides 8 < 3 + 8 --> works. can be a triangle 11 = 3 + 8 --> cannot be a triangle
If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order? (1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered (2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered
B Given: {Cola} + {Beer} + {Ale} = 63. Question: {Cola} = ? (1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered --> {Beer} = 0.8{Ale} --> 5*{Beer} = 4*{Ale} ({Beer} is a multiple of 4 and {Ale} is a multiple of 5). If {Beer} = 4 and {Ale} = 5, then {Cola} = 54 but if {Beer} = 8 and {Ale} = 10, then {Cola} = 45. Not sufficient. (2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered --> {Cola} = 0.75*({Beer} + {Ale}) --> {Beer} + {Ale} = 4/3*{Cola} --> {Cola} + 4/3*{Cola} = 63. We can solve for C. Sufficient.
Does the integer k have a factor p such that 1<p<k? (1) k > 4! (2) 13! + 2<= k <= 13!+13
B. note that k will have a factor p if and only if k is not a prime number. 1) insufficient. since k > 4!, k > 24. k may or may not be a prime number ex k= 27 has factors but k = 29 does not 2) from this it becan be concluded that k could be any of twelve integers, 13! + 2, 13! + 3... 13! + 13. 2 is a factor of 13! + 2, since it is both a factor of 13! nd 2. same for 3 and on. SUFFICIENT. must have a factor in there that works
The cause of the wreck of the ship Edmund Fitzgerald in a severe storm on Lake Superior is still unknown. When the sunken wreckage of the vessel was found, searchers discovered the hull in two pieces lying close together. The storm's violent waves would have caused separate pieces floating even briefly on the surface to drift apart. Therefore the breakup of the hull can be ruled out as the cause of the sinking. Which of the following is an assumption on which the argument depends? A. Ships as large as the Edmund rarely sink except in the most violent weather. B. Underwater currents at the time of the storm did not move the separated pieces of the hull together again. C. Pieces of the hull would have sunk more quickly than the intact hull would have. D. The waves of the storm were not violent enough to have caused the ship to break up the surface. E. If the ship broke up before sinking, the pieces of the hull would not have remained on the surface for very long.
B. what must be true in order for the given premises to justify the conclusion that the broken hull did not sink the ship? if the hull was in pieces during the storm, the waves would have made the pieces drift apart, but they were found close together. so, must not have bene in separate pieces when the ship sank. assumes that since the two pices of the hull were found together, the storm waves never made them drift apart. B- the argument assumes that the piece of the hulls never drifted apart in the first place and hence that underwater currents did not move them back together
The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number of car-crash fatalities per highway mile driven by cars. Which of the following, if true about the United States between 1995 and 2000, most helps to explain why the fatality rate decreased in spite of the increase in average highway speeds? (A) The average number of passengers per car on highways increased. (B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices. (C) The increase in average highway speeds occurred as legal speed limits were raised on one highway after another. (D) The average mileage driven on highways per car increased. (E) In most locations on the highways, the density of vehicles on the highway did not decrease, although individual vehicles, on average, made their trips more quickly.
B. B. more seatbels and airbags would have reduced avg number of fatalities per car accident, resulting in fewer fatalities per mile drive even if higher speeds result in more accidents d. fewer accidents per
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes (1) The cost of the phone call was less than $4.16 (2) The cost of the phone call was greater than $3.35
B. the cost is .75 + .2*(n-3) a call that lasts more than 15 mins should be greater than .75 + .2*(15 -3) = .75 + .2*(12) = .75 + 2.4 = 3.15 1. insufficient. 2. sufficient. it was greater than 3.15, so it lasted longer than 15 minutes
If x is an integer greater than 1, is x equal to the 12th power of an integer ? (1) x is equal to the 3rd Power of an integer (2) x is equal to the 4th Power of an integer.
C. (1) x is equal to the 3rd Power of an integer --> x=m3x=m3 for some positive integer mm. If mm itself is 4th power of some integer (for example if m=24m=24), then the answer will be YES (since in this case x=(24)3=212, but if it's not (for example if m=2m=2), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that x4=m12x4=m12. (2) x is equal to the 4th Power of an integer --> x=n4x=n4 for some positive integer nn. If nn itself is 3rd power of some integer (for example if n=23n=23), then the answer will be YES (since in this case x=(23)4=212x=(23)4=212), but if it's not (for example if n=2n=2), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that x3=n12x3=n12. (1)+(2) Divide (i) by (ii): x=(mn)12=integerx=(mn)12=integer. Now, mnmn can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore mnmn must be an integer, hence x=(mn)12=integer12x=(mn)12=integer12. Sufficient. Answer: C.
Consumer advocate: It is generally true, at least in this state, that lawyers who advertise a specific service charge less for that service than lawyers who do not advertise. It is also true that *each time restrictions on the advertising of legal services have been eliminated, the number of lawyers advertising their services has increased and legal costs to consumers have declined in consequence.* However, eliminating the state requirement that legal advertisements must specify fees for specific services would almost certainly increase rather than further reduce consumers' legal costs. Lawyers would no longer have an incentive to lower their fees when they begin advertising and if *no longer required to specify fee arrangements, many lawyers who now advertise would increase their fees.* In the consumer advocate's argument, the two portions in boldface play which of the following roles? (A) The first is a generalization that the consumer advocate accepts as true; the second is presented as a consequence that follows from the truth of that generalization. (B) The first is a pattern of cause and effect that the consumer advocate argues will be repeated in the case at issue; the second acknowledges a circumstance in which that pattern would not hold. (C) The first is a pattern of cause and effect that the consumer advocate predicts will not hold in the case at issue; the second offers a consideration in support of that prediction. (D) The first is evidence that the consumer advocate offers in support of a certain prediction; the second is that prediction. (E) The first acknowledges a consideration that weighs against the main position that the consumer advocate defends; the second is that position.
C. main argument: if lawyers are not req to specify fees in ads, legal costs likely to rise for consumers. 1st statement is a cause and effect statement about ads and falling consumer costs 2nd gives a reasoning for the conclusion drawn by the advocate. explains why that relation will change
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd? A) 1/4 B) 3/8 C) 1/2 D) 5/8 E) 3/4
C. since 50 odd and 50 even, prob of selecting odd ball at random is 1/2. for the sum of the three numbers to be odd, all must be odd or exactly one must be odd and 2 even. 1) prob of odd odd odd = 1/2*1/2*1/2 = 1/8 2) prob of selecting odd even even= 1/2*1/2*1/2 = 1/8 3) prob selecting even odd even = 1/8 4) prob selecting even even odd = 1/8 1/8* 4= 1/2
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? A. 5/12 B. 2/5 C. 1/2 D. 3/4 E. 5/6
C. It is a circle inscribed in a square. Square side=24---> square(table) area=24^2 Circle diameter=20---> Circle area=PiR^2=100Pi (where Pi=~3.14) covered fraction=100*3.14/24*24=~314/24*24=13/24~1/2
The golden crab of the Gulf of Mexico has not been fished commercially in great numbers, primarily on account of living at great depths-- 2,500 to 3,000 feet down. (A) on account of living (B) on account of their living (C) because it lives (D) because of living (E) being they live
C. IT
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? A. 1/4 B. 3/8 C. 1/2 D. 5/8 E. 3/4
D n(n+1)(n+2)) is divisible by 8 in two cases: A. n=even, in this case n+2=even too and as n and n+2 are consecutive even integers one of them is also divisible by 4, so their product is divisible by 2*4=8; B. n+1 is itself divisible by 8 from here u can also think this way (though it is a lil bit similar) find how many numbers are divisible by 2 or 8 96/2=48 96/8=12 (48+12)/96=60/96=5/8
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? A. 20 B. 40 C. 50 D. 80 E. 120
D "If a committee of 3 people is to be selected" Combo box arrangement (_)(_)(_)/3! "from among 5 married couples" Bag of 10 choices: A,B,C,D,E,F,G,H,I,J "so that the committee does not include two people who are married to each other" First slot has 10 choices (10)(_)(_)/3! but the choice eliminates the spouse. The second slot has 8 choices (10)(8)(_)/3! but the choice eliminates another spouse. The third slot has 6 choices (10)(8)(6)/3! "how many such committees are possible?" (10)(8)(6)/(3*2) = 80
If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points? A. 20 B. 30 C. 40 D. 70 E. 90
D * * * * * (line B) * * * * (line A) Choose 2 points from line A and a point from line B: = 4!/2!2! * 5!/1!4! = 30 Choose 1 point from line A and 2 points from line B: = 4!/1!3! * 5!/2!3! = 4 * 10 = 40 Combine possiblities: 30 + 40 = 70
A certain wooded lot contains 56 oak trees. How many pine trees does the lot contain? (1) The ratio of the number of oak trees to the number of pine trees in the lot is 8 to 5. (2) If the number of oak trees were increased by 4 and the number of pine trees remained unchanged, the ratio of the number of oak trees to the number of pine trees in the lot would be 12 to 7.
D Given: Oak = 56 Pine = ? 1) SUFF O: P = 8x: 5x x = 7 --> 35 2. SUFF (O + 4) : P= 12x : 7x 60:P = 12x: 7x x= 5, P = 35
Unlike computer skills or other technical skills, there is a disinclination on the part of many people to recognize the degree to which their analytical skills are weak. (A) Unlike computer skills or other technical skills, there is a disinclination on the part of many people to recognize the degree to which their analytical skills are weak. (B) Unlike computer skills or other technical skills, which they admit they lack, many people are disinclined to recognize that their analytical skills are weak. (C) Unlike computer skills or other technical skills, analytical skills bring out a disinclination in many people to recognize that they are weak to a degree. (D) Many people, willing to admit that they lack computer skills or other technical skills, are disinclined to recognize that their analytical skills are weak. (E) Many people have a disinclination to recognize the weakness of their analytical skills while willing to admit their lack of computer skills or other technical skills.
D. * "have a disinclination to recognize" is wordy/unidiomatic, and is definitely inferior to "are disinclined to recognize". * if you're going to use "while" with an adjective phrase (while willing to...), then that adjective phrase should precede the main verb. i.e., many people, while willing to... , are disinclined to... * there's also a slight change in meaning. "recognize that their ... skills are weak" just means that the people should know that they have weak skills. "recognize the weakness..." means that they should actually be able to point out the specific weakness.
Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied during a certain show? (1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row for the front 20 rows. (2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows.
E obvious why 1 and 2 are insufficient. together, it is possibly tov ary the number of occupied seats in rows 11-20 (the overlap)
Displays of the aurora borealis, or "northern lights", can heat the atmosphere over the arctic enough *to affect the trajectories of ballistic missiles , induce electric currents that can cause blackouts in some areas and corrosion in north-south pipelines.* A.to affect the trajectories of ballistic missiles,induce B. that the trajectories of ballistic missiles are affected,induce C. that it affects the trajectories of ballistic missiles are affected and induces D.that the trajectories of ballistic missiles are affected and induces E. to affect the trajectories of ballistic missiles and induce
E. D is wrong because "that" violates the correct idiom can heat...enough to affect; the verbs illogically change tenses
A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book? (1) Joe bought 2 paperback books and 3 hardcover books for $12.50. (2) Paul bought 4 paperback books and 6 hardcover books for $25.00.
E. 1. insuff. 2p + 3h = 12.50. not suff 2. insuff. 4p + 6h = 25. insuf together: same equation that cannot be solved, taken together they cannot determine the cost of 1 of each type of book
If s and t are nonzero integers, is s = 1? 1) st = 1 2) st = t
In S1, we might have s=t=1, or s=t=-1, so S1 is not sufficient. In S2, we have: st = t st - t = 0 t(s-1) = 0 which is true either if t=0, or if s=1. We are told t is not zero, so it must be that s=1, which is what the question asked, and the answer is B
If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following? A. 1/12 B. 1/10 C. 1/8 D. 1/6 E. 1/4
K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48. each of the last 5 are less than 1/43, K < 6/43. likewise, since each of the first 5 are greater than 1/48, K > 6/48 = 1/8. thus, 1/8 < K < 6/43. 6/43 < 6/42 = 1/7 so K lies between 1/8 and 1/7. 1/8 is the better answer
If y = |x + 7| + |2 - x|, is y = 9? (1) x < 2 (2) x > -7
Statement (1) says that x < 2. Is y = 9 for all x's less than 2? If we plugged a few values for x less than 2, i.e. x = 1, 0, -1, we might come to the hasty decision that in fact y is always equal to 9 when x < 2. The problem with this set of numbers, however, is that it doesn't do justice to the critical regions in the problem. For statement (1) we must check values not only less than 2 but also less than -7. Otherwise we are artificially restricting the statement to one of the three critical ranges for the problem. In fact when we check x = -10, we see that y is not equal to 9, so statement (1) is not sufficient. The same process can be applied when looking at statement (2) on its own. We must try values of x that fall in the two critical regions which meet the criteria in the statement. Thus, we must test values in the region -7 < x < 2 and values in the region x > 2. When we do, we find that y is not always equal to 9. When we look at the two statements together, the only critical region to be considered is -7 < x < 2. Now the two statements are sufficient (y is always 9 in this region) and the correct answer is C, statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y? A. 0 B. 25 C. 50 D. 75 E. 100
Sum of evenly spaced integers = (number of integers) * (average of biggest and smallest) x is the sum of first 50 positive even integers. Smallest = 2. Biggest = 100. Average of biggest and smallest = (100+2)/2 = 51. Thus: x = (number of integers)(average of biggest and smallest) = (50)(51). y is the sum of first 50 positive odd integers. Smallest = 1. Biggest = 99. Average of biggest and smallest = (99+1)/2 = 50. Thus: y = (number of integers)(average of biggest and smallest) = (50)(50). Thus: x-y = (50)(51) - (50)(50) = 50(51-50) = 50. The correct answer is C
p/q > 1
The inequality p/q > 1 does not necessarily imply that p > q (unless q is positive).
what is the probability that when you flip a coin 5 times you will get 3 heads and 2 tails?
The number of different scenarios is the number of different orderings of HHHTT which, using the skills we learned earlier in this series, is equal to 5!/(3!2!) or 10. The probability of any ONE of these 10 scenarios occurring is equal to 1/2 x 1/2 x 1/2 x 1/2 x 1/2 or 1/32. To find the total probability, simply add up the probabilities of each of the 10 scenarios. This is equal to 10 x 1/32 or 10/32, which simplifies to 5/16.
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods? A. 71 B. 77 C. 80 D. 83 E. 89
We know that there are 3 metal rods with an average length of 77 inches. Total length=77*3=231 inches Shortest rod length=65 inches the sum of lengths of the two longer rods=231-65=166 Since, the longer rods have to be longer than 65, the smallest value one of these longer values could have is 66. Now the question asks us for the longest median value. The median value is the middle value when the three rods are arranged in ascending order of lengths. There are two ways of finding these values 1. Since we need to find the largest middle value, the two longer rods need to be of equal length. If both values are equal in length the middle value will be the largest possible value and the longest rod will be of the same length as the rod of median length. Hence, 2x =166 implies x=83. Maximum length of the median rod=83 2. Testing the values given Let us test the values from the bottom e=89 166-89=77. Since 77 is less than 89, it cannot be the median value. WRONG d=83 166-83=83. Both the rods are of the same length. Hence, this is the largest possible middle value.
If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+1) for all positive integers n, what is the third term of the sequence? A. 3 B. 4 C. 6 D. 8 E. 9
a1, a2, a3 are the first 3 terms. since s1 = a1 and s1 = 1(2)= 2, it follows that a1 = 2. since s2= a1 + a2 --> 2 + a2 and s2 = 2*3 = 6, it follows that 6 = 2 + a2 , a2 = 4. S3 = 3*(4) = 12. 12 = 2 + 4 + a3 = --> a3 = 6
candidate P and Q event
check screenshots
kaxna artifacts
look at problem on gmat prep
rectangular carpet check screenshots
screenshots
|x - y|
the distance of x from y
