Each dinner at Restaurant X includes a pair of side dishes, which

Question

﻿Each dinner at Restaurant X includes a pair of side dishes, which a customer chooses by selecting any one side dish from list A and any one side dish from list B. There are a total of 18 possible pairs of side dishes, and no side dish appears on both lists. If there are fewer side dishes on list A than on list B, how many side dishes are on list B ?

(1) There are a total of 9 side dishes on the two lists.
(2) There are a total of 3 side dishes on list A.

gmatophobia · Accepted Answer

Number of side dishes in List A = x

Number of sides dishes in List B = y

x * y = 18

Possible combinations of (x,y) = 
(1,18)
(2,9)
(3,6)
(6,3)
(18,1) ﻿

We have to remove the possibility of (6,3) and (18,1).

Possible combinations of (x,y) = 
 (1,18)
(2,9)
(3,6) 
 (6,3)
(18,1) ﻿

Statement 1

(1) There are a total of 9 side dishes on the two lists.

Out of the three possible pairs indicated in green, the only possible pair of (x,y) = (3,6).

Hence, we have a definite answer to the question, and statement 1 alone is sufficient. We can eliminate options B, C, and E.

Statement 2

(2) There are a total of 3 side dishes on list A.

The statement provides us with the value of  x .

x = 3.

Hence,  y = 6.

(x,y) = (3,6) .

We have a definite answer to the question, and statement 2 alone is sufficient.

Option D

JeffTargetTestPrep · Answer

Since there is no overlap between the two lists, and since we need to select one item from each of the two lists to make a pair of side dishes, we have: number of pairs = number of items on list A × number of items on list B = a × b We know that ab = 18 and a < b and need to answer the question: b = ? Statement One Alone: => There are a total of 9 side dishes on the two lists. a + b = 9 From the question stem we know that a and b are integers greater than 1 , ab = 18, and a < b, so we have only two cases to evaluate: If a = 2 and b = 9, then a + b ≠ 9, so this is an invalid case. If a = 3 and b = 6, then a + b = 9, so this is the only valid case, and thus there are 6 side dishes on list B. Statement one is sufficient. Eliminate answer choices B, C, and E. Statement Two Alone: => There are a total of 3 side dishes on list A. a = 3 From the question stem, we know that we have only two cases to evaluate: If a = 2 and b = 9, then a ≠ 3, so this is an invalid case. If a = 3 and b = 6, then a = 3, so this is the only valid case, and thus there are 6 side dishes on list B. Statement two is sufficient. Answer: D

GMATinsight · Answer

Given: 
Possible pairs = 18 
 Possible pairs = A*B  
 i.e. A*B = 18 
 Also, A < B

Possible Pairs of {A, B) = (1, 18) (2, 9) (3, 6)

Question: B = ?

Statement 1  : A+B = 9
i.e A = 3 and B = 6 (only possible solution out of the above three cases)

SUFFICIENT

Statement 2  :A = 3
i.e A = 3 and B = 6 (only possible solution out of the above three cases)

SUFFICIENT

Answer: Option D

ITERM · Answer

no options visible?

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

MrMaxMan · Answer

Think about FCP
You have essentially 2 bags you're picking 2 items from, and can make a total of 18 pairs.
You can use FCP to visualize.
Also that the first list is smaller than the second.

(__)x(__) = 18

two variables multiplied to make 18 can be:
(1,18), (2,9), (3,6)
Since A<B, these are our only pairs. You cannot flip them.

I) There's a total of 9 dishes between both lists.
The only pair that sums to 9 is (3,6)
Single solution.
 SUFF.

II) There are 3 dishes on list A.
The only pair where list A has 3 dishes is pair (3,6)
Single solution.
 SUFF.

Each dinner at Restaurant X includes a pair of side dishes, which

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Each dinner at Restaurant X includes a pair of side dishes, which

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