GRE math

10. What positive value for k would make the following the equations of a pair of parallel lines on the same coordinate axes? y = kx - 2 and ky = 9x - 7

Correct Answer: 3 Explanation: First rearrange the second equation to fit the form y = mx + c, where m = slope We get y = (9/k) x - 7/k Parallel lines have the same slope. From equation 1, slope = k From equation 2, slope = 9/k . Equating the two slopes we get k = 9/k; k² = 9; k = 3

2^30 + 2^30 + 2^30 + 2^30 = A. 8^120 B. 8^30 C. 2^32 D. 2^30 E. 2^26 Correct Answer: C

All four terms are identical therefore we have 4 (2^30). But 4 = 2^2, and so we can write 2^2 X 2^30 Which is equivalent to 2^32

3. If S is the sum of 8,6,4,2 and x, what must be the value of x for x to equal 1/5 S ?

Correct Answer: 5 Explanation: If x = 1/5 of the sum, then 8 + 6 + 4 + 2 = 4/5 of the sum. So 20 = 4/5 of S, and 20/4 is 1/5 of S = 5

6. If one edge of a 6-inch ruler is to be marked in 1/10 inch units, how many marks will there be on the edge including the 0 and 6 inch marks?

Correct Answer: 61 Explanation: There are sixty tenths to be marked. This will require 61 marks, because you will need a mark for zero. (If you still do not understand, draw out a ruler and count how many marks for two inches, which will be 20 + 1).

3. The diagonal of a rectangle (left) Half the perimeter of the same rectangle (right) A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information

Correct Answer: B Explanation: The diagonal of a rectangle cuts the rectangle into two equal triangles. The diagonal is the hypotenuse of either of these triangles, and must be less than the sum of the other two sides. The other two sides make up half the perimeter, which is, therefore, greater.

9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip? http://www.majortests.com/gre/problem_solving_expl.php?exp=503130312439243437 A. 10 B. 8 C. 6 D. 4 E. 2

Amy can travel clockwise or anticlockwise on the diagram. Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes. Similarly, anticlockwise she has four different routes. Total routes = 8

The percentage of the multiples of 2 that are also multiples of 5 (left) The percentage of the multiples of 5 that are also multiples of 2 (right) A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information

Correct Answer: B Explanation: The only multiples of 2 that are multiples of 5 are the multiples of 10. So only 1 in 5 multiples of 2 are multiples of 5. (Check it out..2,4,6,8,10,12,14,16,18,20...) The multiples of 5 that are multiples of 2 are also the multiples of ten. But this time, half the multiples of 5 are multiples of 2. (Check it out...5,10,15,20,25,30.....)

The distance between the points with rectangular coordinates (0,5) and (0,10) (Left) The distance between the points with rectangular coordinates (1,8) and (-3,5) (right) A. The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct Answer: C

Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance d between these points is given by the formula: d=√sqrt[(x2-x1)^2+(y2-y1)^2] ​ ​​ ​ ​​

http://www.majortests.com/gre/problem_solving_expl.php?exp=50313031243130243233 10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ? A. 18 B. 13.5 C. 9 D. 4.5 E. 3 Correct Answer: D

If we take AE as the base of triangle AEC, then the height is CD. The height of the triangle is therefore, 9 (given). To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1. The area of AEC = ½ base x height =1/2 x 9 = 4.5

8. Given that the sum of the odd integers from 1 to 99 inclusive is 2500, what is the sum of the even integers from 2 to 100 inclusive?

If you write out part of each series like this 1,3,5,7... 2,4,6,8... You will see that every term in the second series is one more than the corresponding term in the first series. Since there are 50 terms, the second sum will be 50 more than the first = 2500 + 50 = 2550

1. 145 300 610 1230 In the above sequence every term after the first is formed by multiplying by x and then adding y, where x and y are positive integers. What is the value of x + y?

Look for a simple relation between the numbers. So if we try multiplying by 2, then 145 becomes 290, to which we need to add 10 to make 300. (If we tried multiplying by 3 the number would be too large. Check with the third term; doubling 300 gives 600 and adding 10 gives 610. So this is the relation, and x = 2 , and y = 10. x + y =12

5. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course? A. 6 B. 15 C. 24 D. 33 E. 54

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither 78 = (41-9) + (22-9) + 9 + neither. Not enrolled students = 24

2. A confectioner has 500 mint, 500 orange and 500 strawberry flavored sweets. He wishes to make packets containing 10 mint, 5 orange and 5 strawberry sweets. What is the maximum number of packets of this type he can make?

Since every packet must have 10 mints, this is the limiting factor since the mints will be used up first. 500/10 gives the number of sets of mints = 50 packets can be made.

6. A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot). Indicate ALL such answers. A. 17 B. 28 C. 35 D. 39 E. 50 Correct Answer: ABDE

The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P). Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17; if n= 5, length = 28, etc.but there is no whole number that can give 35. Hence all the answers except C are correct.

5. What is the maximum number of points of intersection of four distinct lines in a plane?

Two lines have one point of intersection. A third line can cut through the other two to give two new points of intersection. (Total = 3). A fourth line can cut through the other three giving three new points of intersection (Total 3 + 3 = 6)

4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? A. 48 B. 32 C. 24 D. 18 E. 12

V= a^3 The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.