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(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

(1) AD= 20

(2) AB = CD

**Solution:** Knowing that AD= 20 makes statement one as insufficient. We have to think about evaluating the statements above in combination. They are not sufficient in isolation nor are they sufficient in combination.

The correct answer is (E).

(1) There is a total of 20 women and men in the room.

(2) The number of men in the room equals the square of the number of women in the room.

**Solution:** In isolation, statement one is insufficient. If we evaluate them in combination, we can plug in numbers and see if that works.

The correct answer is (C).

(1) n > 4

(2) n^2 = 25

**Solution:** (100-5)/5, but what if n = 6 : (100-6)/6? We have one case where we get an integer and the other where it is not an integer.

What about statement two? If n^2 = 25 then there are two possible values for n, n can equal positive or negative 5. If we plug in those numbers then both possible values of n give you an integer.

The correct answer is (B).

(1) When the shop opened last Friday there were 160 sweaters in its inventory.

(2) All but 40 sweaters in the shop's inventory were sold last Friday.

**Solution:** Statement one is sufficient. Statement two is also sufficient.

Therefore the correct answer is (D).

(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2:1.

(2) Of the first 6 marbles removed, 4 are red.

**Solution:** Statement one is sufficient. Statement 2 is not sufficient because we don't know about the remaining two marbles' colors.

The correct answer is (A).

(1) w and z are positive integers.

(2) w and z are consecutive odd integers.

**Solution:** Statement 1 is not sufficient. The only possibly consecutive odd integers are 13 and 15, and if you know this then you can work out the value of w times z.

The correct answer is (B).

(1) x(a + b) = 3

(2) a = b = 1.5 and x = 1

**Solution:** Generally speaking, you don't want to do that much scratch work, but this question does require scratch work. x(a + b) = 3 à ax + bx = 3 à ax = 3-bx, so statement one is sufficient in isolation.

Statement two is also sufficient in isolation, therefore the correct answer is (D).

(1) x is a prime number.

(2) 31 ≤ x ≤ 37

**Solution:** Statement one is not sufficient in isolation and statement two in isolation is also not sufficient. In combination, 31 and 37 are prime numbers, so statements one and two are insufficient.

The correct answer is (E). You need to know all of the prime numbers up to 37 for the GMAT.

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