JL = KM
| JK | LM |
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Solution
Imagine that JL and KM are two pencils of equal length. Now imagine putting them side by side and altering the amount of overlap (the region between K and L). The overlap region is identical for both pencils and so the amount not overlapping is also equal no matter how large of small you make KL. So JK and LM are always equal.
| The area of a right angled triangle with sides 6,8 and 10 | Twice the area of a right angled triangle with sides 3,4 and 5 |
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Solution
The area of the triangle on the left is ½.6.8 = 24 (10 is the hypotenuse)
The area of one of the triangles on the right is ½.3.4 = 6; and so two of them will have an area of 12, which is much smaller.
| The percentage of the multiples of 2 that are also multiples of 5 | The percentage of the multiples of 5 that are also multiples of 2 |
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Solution
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.....)
A fair coin is tossed three times
| The chances of getting 3 heads | The chances of getting no heads |
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Solution
A fair coin is equally likely to result in heads as tails. The right column is the equivalent of getting three tails, which has the same probability as getting three heads.
| + 7 | √(36 + 49) |
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Solution
The right column is the root of the sum of 36 and 49, which is √85. This will obviously be more than 7 (Do not work out more than needed).
Note: On the GRE the square root sign ALWAYS refers to the positive root.
| The distance between the points with rectangular coordinates (0,5) and (0,10) | The distance between the points with rectangular coordinates (1,8) and (-3,5) |
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Solution
Make a rough sketch. On the left hand side, both points are on the y-axis, and are 5 units apart. The line joining the points on the right hand side forms the hypotenuse of a triangle with sides 4 (parallel to the x-axis), and 3 (parallel to the y-axis). This means the hypotenuse must be 5 (3-4-5 triangle). So both columns are equal.
x + y = 5
y – x = 3
| x | y |
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Solution
This is a pair of simultaneous equations. Just add them together to get 2y = 8
So y = 4. Putting this value in the first equation gives x + 4 = 5
So x = 1. The right hand column is greater.
| The diagonal of a rectangle | Half the perimeter of the same rectangle |
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Solution
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.
n is an integer > 0
| 1/n + n | 2 |
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Solution
We can read the left column as a positive integer plus a fraction. If the integer n is 1, this will give us a total of 2; for larger integers like 3, we will get 3 + 1/3, which is bigger than two. Since we have two different results (one with the two columns equal, and one with them different) we have a D answer choice.
The average (arithmetic mean) of four numbers is 36
| The sum of the same four numbers | 140 |
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Solution
If the average of a set of numbers is known, we can multiply the average by the number of elements in the set to find the total. Here if the average is 36, the total of the four numbers is 144. Hence, this is bigger than 140. Answer A.