Question: A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?

1. 5 pencils and 3 pens cost 30 cents
2. 4 pencils and 4 pens cost 32 cents

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

S1:
5 * pencils + 3 * pens = 30 cents
Only 5 * 3 + 3 * 5 = 30 satisfies the equation in which pencil costs 3 cents and pen costs 5 cents
Sufficient

S2:
4 * pencils + 4 * pens = 32
Pencils + pens = 8
Could be 4 + 4 = 8 or 5 + 3 = 8 and so on
Insufficient

Correct Option: A

Approach Solution (2):

Let express the cost of the pen = x
And cost of the pencil = y

S1: 5x + 3y = 30; y should be multiple of five and none of the variables can be 0; 5 is the only integer which satisfies the equation, the next multiple of five is 10 and it’s not valid as x must be 0 at that case.
Sufficient

S2: 4x + 4y = 32;
4(x + y) = 32
x + y = 8
Many pairs are possible
Insufficient

Correct Option: A

Approach Solution (3):

Let x = the cost of a pencil and y = the cost of a pen

S1: We can write this as 5x + 3y = 30. At the first glance it make look unsolvable because there are two variables; however, there is only one solution since the prompt said we can only use “non-zero whole numbers”, i.e. integers
This equation only works when x = 3 and y = 5; therefore 5x = 15
Sufficient

S2: We can write as 4x + 4y = 32 and then simplify it to x + y = 8
There are many possible values of x
Insufficient

Correct Option: A

“A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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