FDP for GMAT Drill
What number is 62.5% of 192?
Recognize that 62.5% = .625 = 5/8 5 × 192 − 8 The 8 cancels out the 192 evenly by 24 5 × 24 = 120 ∴120 = 62.5% × 192
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 percent protein and food Y contains 15 percent 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
Recognize they want in grams so convert X & Y numbers to grams. If mix was all X, then out of the 300g of food, 30 would be protein (10% × 300) If mix was all Y, then out of the 300g of food, 45g would be protein (15% × 300) Those 2 numbers make either end of your number line X = 30⁻⁻⁻Goal = 38 ⁻⁻⁻ Y = 45 |−−−−−−−−−−|−−−−−−−| Total distance possible = 15 (denominator) How much X pulled = 7 (45−38) = 7/15 How much Y pulled = 8 (38−30) = 8/15 Since X is 7/15 of the 300g mix, multiply the two together: 7/15 × 300 → cross out 15 & 300 7 × 20 = 140g of food X are used
The Crandalls' hot tub is half filled. Their swimming pool, which has a capacity four times that of the tub, is filled to four-fifths of its capacity. If the hot tub is drained into the swimming pool, to what fraction of its capacity will the pool be filled?
Recognize this is a SMART NUMBERS problem. The easiest way is to find a common denominator between the 2 fractions given and assign that number to the smallest full unit. Between 1/2 and 4/5 the common denominator is 10 so make this the Hot Tub at it's fullest FULL: Hot Tub = 10 Swimming Pool = 40 (4x Hot Tub) CURRENT: Hot Tub = 5 Swimming Pool = 32 (40 × 4/5) ∴5 + 32 = 37 37/40 would be the capacity
What is the units digit of (2)⁵(3)³(4)²?
2⁵ = 32 3³ = 27 4² = 16 Take the units digits and multiply them together: 2 × 7 × 6 = 84 4 is the units digit.
Multiply the numerator of a positive, proper fraction by 3/2 Will this cause the fraction to increase, decrease or will it stay the same?
3/2 is larger than 1 so that will cause a numerator to increase. If a numerator increases while the denominator stays the same then the entire fraction increases.
What is the ratio x:y:z 1) x + y = 2z 2) 2x + 3y = z
This is a COMBO problem REPHRASE: Really just need 2 of x/y or y/z or x/z STATEMENT 1 - No way to manipulate and get rid of a variable so insufficient STATEMENT 2 - No way to manipulate to get rid of a variable so insufficient Combining them you can use substitution to see that you can eliminate a variable and get the ratio of x/y and y/z
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate?
This is a SMART NUMBERS problem Lisa: Income (common denominator) = $24 3/8 = rent = $9 5/12 = food = $10 Charity gets $5 Carrie 2x Lisa's income so = $48 1/4 = rent = $12 1/2 = food = $24 Charity gets $12 Total charity = $17 Total income = $72 17/72 ←
The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A. If Q = 10B−A, what is the value of Q? 1) The tens digit of A is 7 2) The tens digit of B is 6
This is a question that needs to be REPHRASED first A = xy (not multiplied) = 10x + y B = yx (not multiplied) = 10y +x Q = 10(10y+x) − (10x + y) Q = 100y + 10x − 10x −y Q = 99y You only need to know Y STATEMENT 1) This is telling you what X is so insufficient STATEMENT 2 - This is telling you Y - SUFFICIENT
A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?
This is another number line problem |−−−−−−−|−−−−−−−−−| A = 40 Goal = 50 → B = 65 Total distance is 25 so that's the denominator A pulls 15 it's direction = 15 / 25 = 3 / 5 = 60% B pulls 10 it's direction = 10 / 25 = 2 / 5 = 40% Brand A is 60% of the total mix
A bowl is half full of water. Four cups of water are then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?
Get everything in percents: Original = 50% Now = 70% Set up a proportion: Adding 4 cups increased amount by 20% therefore 4 = 20% 20 4 −− = −− 100 x 1/5 = 4/x x = 20 Alternatively... 4 x −− = −− 20 50 x = 10 which is what 50% was Now add 10 (original) + 4 (new) = 14 = 70%
A 500 mL solution is 20% alcohol by volume. If 100 mL of water is added, what is the new concentration of alcohol, as a percent of volume?
Make a chart that shows the progression from original to new. ml→→→Original→→→Change→→→New Water→400 mL−−−−− 100mL−−−−− 500mL Alcohol→100mL−−−−−−0 mL−−−−−−100mL Total→→500mL−−−−−−100mL−−−−−600mL Alcohol / Total = 100/600 = 1/6 = .167 = 16.7%
Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually. After 3 years, what is the balance on the account? (Assume Lori makes no deposits or withdrawals)
$13,310 10,000 × 1.1 = 11,000 11,000 × 1.1 = 12,100 12,100 × 1.1 = 13,310 ←
Express the following as percents: 1000/10 25/8
1000/10 should be multiplied by 10 to get it over 100 - 10,000/100 and as a percent that is 10,000% 25/8 = (25 ÷ 8) × 100 = 3.125 ×100 = 312.5%
200 is 16% of what number?
200 = (16/100) × n 16/100 = 4/25 200/(4/25) = 200 × (25/4) Cancel out 4 & 200 leaving 50 × 25 = 1250
Estimate to the closest integer: What is 11/30 of 6/20 of 120?
Could have estimated each of them to closes fraction, but easier to cross multiply: 11/30 × 6/20 × 120 = 30 & 6 cross out 20 & 120 cross out leaving 11/5 × 1/1 × 6/1 = 66/5 ≈ 13
In a box containing action figures of the three Fates from Greek mythology, there are three figures of Clotho for every two figures of Atropos, and five figures of Clotho for every four figures of Lachesis. A) What is the least number of action figures that could be in the box? B) What is the ratio of Lachesis figures to Atropos figures?
C:A = 3:2 C:L = 5:4 A) You would want to combine the ratios to find out how many are in the box, but you can't because there's not common denominator (C). Find a common denominator by multiplying by 3 or 5 to get to 15 for C C:A = 15:10 C:L = 15:12 ∴ C:A:L = 15:10:12 ∴ 15 + 10 + 12 = 37 so that is the least that can be in the box B) 12:10 reduces to 6:5 (already did the work in the problem before
⊗η ×∃η −−−− ∆∃η In the multiplication above, each symbol represents a different unknown digit, and ⊗ × ∃ × η = 36. What is the three-digit integer ⊗∃η ? A) 263 B) 236 C)194 D) 491 E) 452
E is easily eliminated because 4 × 5 × 2 ≠ 36 Left with factors 4, 9, 2, 3, 6 and 1 Make a chart that looks like this and fill in all answer choices along a row: ⊗ = 2 | 2 | 1 | 4 ∃ = 6 | 3 | 9 | 9 η = 3 | 6 | 4 | 1 We know that the ones digit has to equal n × n's ones digit 3 × 3 ≠ 3 so A is out 6 × 6 = 36 so B is possible 4 × 4 ≠ 4 so C is out 1 × 1 = 1 so D is possible At this point we're only left with 2 answer choices and you can bet it will be B because the GMAT will think everyone will pick 1. Still do the math. 26 ×36 −−−− 156 +780 −−−− 936 Remember to check both the ∃ and the η Both work - answer is B
Which of the following fractions will terminate when expressed as a decimal? (choose all that apply) A) 1 / 256 B) 27 / 100 C) 100 / 27 D) 231 / 660 E) 7 / 105
First, fully reduce all the fractions Then look at the ones who's denominators would only have prime factors of 2 & 5 if factored out A) 256 can be written as 2⁸ B) is obvious... D) Once reduced, this is 7/20 and 20 only has prime factors of 2 & 5
What is the length of the sequence of different digits in the decimal equivalent of 3 / 7?
Long division problem 3÷7 = 0.4285714 Length of the string that does not repeat = 6
AB ×CA −−−−− DEBC In the multiplication above, each letter stands for a different non-zero digit, with A × B < 10. What is the two-digit AB? A) 23 B) 24 C) 25 D) 32 E) 42
Look at it carefully - You only need to know C, B and A to solve the problem. All the answer choices represent what AB would be so you know that A and B must be either 2, 3 or 4 Note that A × B < 10 so C is automatically out B × A = C therefore C can only be 6 or 8 and you have enough to solve out As you multiply through, see which answer's 10's digit matches the B in the problem to make it hold true.
800, increased by 50% and then decreased by 30%, yields what number
Never remember the fraction portion, so just do it the scrappy way 800 × 1.5 = 1200 → then decrease this 1200 × 0.7 = 840 840
A and B are both two digit numbers, with A > B. If A and B contain the same digits, but in reverse order, what integer must be a factor of (A−B)? A) 4 B) 5 C) 6 D) 8 E) 9
PLACE VALUE A = xy (not multiplied) B = yx (not multiplied) To get to 52 you would multiply (10×5) + 2 because 5 represents the 10s digit. A = 10x + y B = 10y + x A−B = 10x + y − 10y − x A−B = 9x −9y A−B = 9(x−y) ∴ E) 9
What is the units digit of 7²×9²×3³?
Rewrite so you think of it like this: (7×7)(9×9)(3×3×3) 7×7 = 49 → keep the 9 9×9 =81 → keep the 1 3×3×3 = 27 → keep the 7 Multiply the ones digits together 9×1×7 = 63 →3 is the units digits of the final product
Simplify (given that ab ≠ 0): 12ab³ − 6a²b −−−−−−−−− 3ab
Split in to 2 separate fractions 12ab³ 6a²b −−− − −−−− → cross out everything you can & left with no denominators 3ab 3ab 4b² − 2a
Divide a positive, proper fraction by 3/ 13 Will this cause the fraction to increase, decrease or will it stay the same?
To divide by 3/13 you have to multiply by its reciprocal or 13/3 This means the numerator will increase more than the denominator so the fraction will increase 2/3 × 13/3 = 26/9
Kris-P cereal is 10% sugar by weight, whereas healthier but less delicious Bran-O cereal is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Kris-P cereal to Bran-O cereal, by weight?
The easy way is to draw a number line |−−−−−−−|−−−−−−−−−−−−−−| 2⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻4⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻10 Bran → Goal⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻Kris-P Total movement between 2 & 10 = 8 so that is your denominator Bran pulled the percentage 6 points his way (10−4) so his fraction is 6/8 or 3/4 Kris-P pulled the cereal only 2 points her way (4−2) so her fraction is 2/8 or1/4 ∴ The ratio between the to is the two numerators 3:1 SECOND WAY Make another chart that shows what will happen to K and Bran Since no numbers given in this one, use SMART NUMBERs (for K) - remember you can only use one so use a variable for the second one Ingredients−−−−−−K−−−−−Bran−−−−−−Total Sugar−−−−−−−−−10−−−−−0.02x−−−−−−0.04(100+x) Not Sugar−−−−−−90−−−−−0.98x Total−−−−−−−−−100−−−−−−x−−−−−−−100+x You have your inputs and your goal so now you can set them equal to each other 10 + 0.02x = 0.04(100+x) 10 + 0.02x = 4 + 0.04x → combine like terms 6 = .02x 6/0.02x = 6/(2/100) = 6 × (100/2) → 2 & 6 cancel out → 300 Ratio K:B = 100:300
The ratio of men to women in a room is 3:4. If there are 56 people in the room, how many of the people are men?
Use the "unknown variable" to serve as an amount of people Therefore 3x + 4x = 56 7x = 56 x = 8 Plug back in to original equation where 3x = men = 3(8) = 32
A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?
Use the number line trick again, only use the changes as your end points −13⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻−1⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻5 |−−−−−−−−−−−−−−−−−|−−−−−−−−−−| Pencils⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻Goal⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻Pens Total movement is 5−(−13) = 5+13 = 18 (denominator) Pencils moved the line 6 points Pens moved the line 12 points Ratio of Pens : Pencils = 6:12 or 1:2
Which integer values of n would give the number 2002 ÷ 10⁻ⁿ a value between 1 and 100?
−2, −3 Given 2002 needs to be between 1 and 100 when multiplied by 10 to a power, we know that it can either be 2.002 × 10³ 20.02 × 10² To divide them, you flip the signs and get −2 or −3
Which integer values of n would give the number −37,129 × 10ⁿ a value between −100 and −1?
−3, −4 Given −37, 129 needs to be between −100 and −1 when multiplied by 10 to a power, we know that it can either be: −37.129 × 10⁻³ −3.7129 × 10⁻⁴
