Data Sufficiency

At a certain store, each notepad costs x dollars and each marker 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?
(1) Each notepad costs less than $1.
(2) $10 is enough to buy 11 notepads.

OA E

shrey2287 wrote:At a certain store, each notepad costs x dollars and each marker 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?

Since $10 is enough to buy 5 notepads at $x each and 3 markers at $y each, we get:
5x + 3y ≤ 10.

The question stem asks whether $10 is enough to buy 4 notepads and 4 markers:
4x + 4y ≤ 10
2x + 2y ≤ 5
x+y ≤ 2.5.

Question stem rephrased: Is x+y ≤ 2.5?

(1) Each notepad costs less than $1.
(2) $10 is enough to buy 11 notepads.

It is important to recognize not only how a problem is restricted but also how it ISN'T.
Neither statement restricts the cost of the MARKERS (y).
Try EXTREME values.

If x = .01 and y = .01, both statements are satisfied and 5x + 3y ≤ 10.
In this case, x + y = .01 + .01 = .02, which is less than 2.5.

If x = .01 and y = 3, both statements are satisfied and 5x + 3y ≤ 10.
In this case, x + y = .01 + 3 = 3.01, which is NOT less than 2.5.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.