GMAT Test Prep : Quantitative Data Sufficiency Test

Is the data given in the two statements, labeled (1) and (2), sufficient for answering the question?

All numbers used are real numbers.

1. A building has two types of apartments, big and small. 65 percent of the apartments are small. The number of occupied big apartments is twice the number of unoccupied small apartments. What percent of the apartments in the building are occupied ?

(1) The number of occupied big apartments is six times the number of unoccupied big apartments.

(2) The building has a total of 160 apartments.

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

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

If 65% of the apartments are small, then 35% are big.Statement (1) specifies the ratio of occupied to unoccupied in big apartments is 6:1. This implies that 30% of the building is occupied big apartments. Since it is given that the number of occupied big apartments is twice the number of unoccupied small apartments, 15% of the building is unoccupied small apartments. If 65% of the building is small apartments, then 50% is occupied small apartments. Adding 30% (for occupied big apartments) to 50% (for occupied small apartments) gives 80% for the occupied apartments in the building. Thus, statement (1) ALONE is sufficient.

Statement (2) ALONE is insufficient because the question pertains to percent occupancy, where the actual number of apartments is irrelevant as demonstrated through equations below.

Let S denote the number of small apartments, B the number of big apartments and T the total number of apartments. Further, let subscripts O and U denote occupied and unoccupied. Then, the following equations can be formulated.

SO + SU = 0.65 T (given)

BO + BU = 0.35 T (given)

BO = 2 SU (given)

BO = 6 BU (Statement 1)

The above four equations can be solved to obtain SO and BO in terms of T, and then calculate the required occupancy percent from (SO + BO)/T.

Clearly, the value of T = 160 as given in Statement (2) is not required.

3. A certain electronics store sold 60 percent of the computers in its inventory during the month. What was the total revenue from the sale of the computers?

(1) The computers were sold for an average price of $875 during the month.

(2) All but 34 computers in the store's inventory were sold during the month.

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

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

Statement (1) specifies the average price, but not the number of computers sold. Thus, statement (1) ALONE is not sufficient.

Statement (2) allows calculation of the number of computers sold, but not the price. Thus, statement (2) ALONE is not sufficient.

Since 34 computers are left (which corresponds to 40% of the inventory), the inventory may be calculated (as 85). Then, 60% of this inventory may be multiplied by the average price to obtain the total revenue. Thus, BOTH statements TOGETHER are sufficient.

6.

square

What is the area of square KLMN?

(1) KL = 7 inches.

(2) Its diagonal is √98 inches.

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

EACH statement ALONE is sufficient.

To find the area of square, its side must be known because

Area of square = Side x Side.

Statement (1) specifies the side. Thus, statement (1) ALONE is sufficient.

Statement (2) specifies the diagonal. The side can be found using the Pythagorean theorem and then the area calculated as follows:

KL2 + LM2 = (√98)2

Since KL = LM, 2LM2 = 98 or LM = √49 = 7 inches.

Area of square = 7 x 7 square inches = 49 square inches.

Thus, statement (2) ALONE is sufficient.

8. Is the integer n divisible by 30 ?

(1) n is divisible by 18.

(2) n is divisible by 20.

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

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

If an integer is divisible by 18, it may or may not be divisible by 30. For example, 36 is divisible by 18 but not by 30, whereas 90 is divisible by 18 as well as 30. Thus, statement (1) ALONE is not sufficient.

If an integer is divisible by 20, it may or may not be divisible by 30. For example, 40 is divisible by 20 but not by 30, whereas 60 is divisible by 20 as well as 30. Thus, statement (2) ALONE is not sufficient.

If an integer is divisible by both 18 and 20, then it is necessarily divisible by 30. Since 18 = 2 x 3 x 3 and 20 = 2 x 2 x 5, their LCM (least common multiple) is 180 = 2 x 2 x 3 x 3 x 5. Multiples of 180 are divisible by 30.Thus, BOTH statements TOGETHER are sufficient.

11. A terminating decimal is defined as any decimal that has a finite number of nonzero digits. When the ratio of two positive integers m and n is

expressed as a decimal, is m/n a terminating decimal?

(1) 330 < m < 333

(2) n = 3

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

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

Statement (1) states that m is either 331 or 332. Now, 332/2 (= 166) is a terminating decimal, but 332/3 (= 110.666...) is a recurring decimal (and not a terminating decimal). Thus, statement (1) ALONE is not sufficient.

Statement (2) states that n is 3. If m is a multiple of 3, then m/n is a terminating decimal; otherwise, it is a recurring decimal (ending in .333... or .666...). Thus, statement (2) ALONE is not sufficient.

If m is either 331 or 332 and n is 3, then m/n is necessarily a recurring decimal. Since 331/3 = 110.333... and 332/3 = 110.666..., m/n is not a terminating decimal. Thus, BOTH statements TOGETHER are sufficient.

13. Is x negative ?

(1) x2 > 0

(2) x3 > 0

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

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

Ο BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Ο EACH statement ALONE is sufficient.

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

Answer

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

Statement (1) states that the square of the number x is positive, which implies that x may be positive or negative. Thus, statement (1) ALONE is not sufficient.

Statement (2) states that the cube of the number x is positive, which necessarily implies that x is necessarily positive (and not negative). Thus, statement (2) ALONE is sufficient.