DS - prime numbers

What is the value of the integer x?

(1) x is a prime number.
(2) 31 <= x < 37

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - woman's age (sensitive matter)

In what year was Ellen born?

(1) Ellen's brother Pete, who is 1+1/2 years older than Ellen, was born in 1956.
(2) In 1975 Ellen turned 18 years old.

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - relative movement of two cars

While on a straight road, car X and car Y are travelling at different constant rates. If car X is now 1 mile ahead car Y, how many minutes from now will car X be 2 miles ahead of car Y?

(1) Car X is travelling at 50 miles per hour and car Y is travelling at 40 miles per hour
(2) 3 minutes ago car X was 1/2 mile ahead of car Y

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - algebraic equation

Is ax = 3- bx?

(1) x(a+b)=3
(2) a=b=1.5 and x=1

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - bookrack capacity

I..........x.........I
-------------------
(consider a bookrack with length x)

Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack?

(1) x = 50 centimeters
(2) Twelve of the volumes have an average (average men) thickness of 5 centimeters,

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - number product

If w+z = 28, what is the value of wz?

(1) w and z are positive integers.
(2) w and z are consecutive odd integers

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - triangle internal angles

(consider a triangle with internal angles x, y and z)

Is the triangle equilateral?

(1) x = y
(2) z=60

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - jar with color marbles

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?

(1) Of the marbles removed, the ratio between the number of red ones to the number of blue ones is 2:1.
(2) Of the first 6 marbles removed, 4 are red.

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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

DS - sweaters shop inventory

Last Friday a shop sold 3/4 of the sweaters in its inventory. Each sweater sold for $20. What was the total revenue last friday from the sale of these sweaters?

(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.


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 suffcient, but NEITHER statement alone is sufficient.
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient.

integer, positive int, negative int, whole numbers definition for GMAT

Integers, Natural Numbers and Whole Numbers

The numbers {... −3, −2, −1, 0, 1, 2, 3, ...} form the set of integers.
The notation { } indicates 'set' or collection, and the three dots indicate that the list continues endlessly to infinity.
The numbers {1, 2, 3, 4, ...} form the set of positive integers (also called natural numbers or counting numbers).
The numbers {−1, −2, −3, ...} form the set of negative integers.
The number 0 is an integer which is neither positive nor negative. It is usually not considered a counting number.
The numbers {0, 1, 2, 3, ...} form the set of whole numbers, i.e. the set of positive integers and zero.