At a Certain Bookstore, Each Notepad Costs x Dollars GMAT Data Sufficiency

bySayantani Barman Experta en el extranjero

Question: At a certain bookstore, each notepad costs x dollars and each markers costs y dollars. If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4 markers instead?

Each notepad costs less than $1
$10 is enough to buy 11 notepads

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):

Given: $5x+3y \leq 10$

Question: $4x+4y \leq 10$

Note that both the statements are telling us basically the same thing:

(1) x < 1;
(2) 11x < 10 --- x < $\frac{10}{11} \approx 0.9x$;

Now if both notepad and marker cost very cheap then the answer would be YES but if the notepad costs $0.1 and marker costs $3 then the answer would be NO.

Not sufficient

Correct Option: E

Approach Solution (2):

Let me put it in this way:

Given: $5x+3y \leq 10$

Question: $4x+4y \leq 10$

Note: In both the above cases, we buy total of 8 items. All it is asking is, with the same amount i.e.$10 can I buy more y, making y to 44 items from 3 items, instead 1 x, making x to 4 items from 5 items.
Hence, to answer this question, all we need to know is the price of 1 y less than that of one 1 x.
--- is Y < X. if this is the case, then I can safely replace 1 x with 1 y for that/leass than the amount ($10). Can I?

S1: x < 1. Who cares? I need to know is Y < X
Not sufficient

S2: 11x < 10 --- x < 1, same as above
Not sufficient

S1 and S2 both cannot make the sandwich without the extra stuff.
Hence not sufficient

Correct Option: E

“At a certain bookstore, each notepad costs x dollars and each markers costs y dollars. If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4 markers instead?”- 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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At a Certain Bookstore, Each Notepad Costs x Dollars GMAT Data Sufficiency

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