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?
- 5 pencils and 3 pens cost 30 cents
- 4 pencils and 4 pens cost 32 cents
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- 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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