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- If ½ the result obtained when 3 is subtracted from 7x is equal to the sum of 12 and 4x, what is the value of x ?

- 21
- 22
- -27
- 22
- 9/5

Answer: C

Translate the expression into an equation

If ½ the result obtained when 3 is subtracted from 7x: ½ (7x – 3)

sum of 12 and 4x: 12 + 4x

7x – 3 = 2 (12 + 4x)

x = -27

- Which of the following procedures is always equivalent to finding the average of 5 given numbers?

Select__all__that apply.

- Multiplying the 5 numbers and then dividing the product by 25.
- Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
- Ordering the 5 numbers numerically and then selecting the middle number.

Answer: B

Average is adding the numbers and dividing by 5

A: multiplying 5 numbers will give a very large product and dividing by 25 doesn’t really give the average. Also, if any one of the 5 numbers is 0, the average will become 0 irrespective of the other numbers.

B: Adding the 5 numbers, doubling the sum means instead of dividing the sum by 5 we are multiplying by 2 so effectively the average has been multiplied by 10

Moving the decimal point one place to the left brings us back to the average. SELECT.

C: Ordering the 5 numbers numerically and then selecting the middle number will give you the average only if you have numbers in sequence that are equally spaced.

- In the addition problem above, if X and Y each represent a digit, then what is X?

Answer: 9

Solution: These questions used to be quite frequent on the old GRE they don’t appear often now.

Don’t be surprised by the format. It is actually quite easy.

Look at the left-most column (the Hundreds place) X + 2 results in 2 and a carryover that is Y. So Y is 1

Also X + 2 ends in 2 which means the column addition is 10 + 2 but X cannot be 10, so X is 9.

Verify with x = 9 and Y= 1

- If a = 2x, b = 2x/3, c = 2ab, and d = (a+2b) / (bx+c) what is d in terms of x

- x
- 1/x
- x
^{2} - 1/x
^{2} - 2x/3

Answer: B

c = 2ab = 2.2x.2x/ 3 = 8x^{2}/3

a+2b = 2x +4x/3 = 10x/3

bx+c = (2x/3).x + 8x^{2}/3 = 10x^{2}/3

d = (10x/3)/(10x^{2}/3) = 1/x

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- 3a + 5
- 3a – 9
- 3a + 10
- 3a – 4
- 3a + 4

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