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?

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

How to solve above problem quickly?

this is a weird problem.

try to attack the problem from a conceptual standpoint first. there are 2 issues:
- the absolute prices of the items (if they're dirt cheap, then $10 will be good enough regardless)
- whether a marker is more expensive than a notepad (notice that you're 'trading' one notepad for one marker, and wondering whether that transaction will cause you to go over the $10)

notice that choice (2), which means that each notepad costs $10/11 = $0.91 or less, IMPLIES choice (1). that makes the following choices impossible, without even looking at the problem:
* A is impossible (because if (1) is sufficient then (2) must also be sufficient)
* C is impossible (because (1) and (2) together is the same thing as just (2))

let's just consider EXTREME cases:
(a) make the markers really expensive
- let's make notepads cost a penny each (which definitely satisfies both criteria), and make markers $3 each. then $10 is not enough for four of each.
(b) make everything really cheap
- if everything costs a penny, then $10 will buy you whatever you want.

answer = e

May you explain a little bit more on why the ST2 is not sufficient??

Thanks

Given 5x + 3y < 10
Is 4x + 4y < 10 ??

Statement 1:
x < 1
assume x = 0.9
4.5 + 3y < 10
y < 1.83
x + y < 0.9 + 1.83 = 2.73
4(x + y) < 10.92
4(x + y) may take 9, 10, or 10.9. So, $10 may or may not be sufficient.
Insufficient

Statement 2:
x < 10/11
x < 0.91
assume x = 0.9 as in statement 1
Insufficient

Statement 1 and 2
x < 1 and x < 0.91 implies x < 0.91 as in statement 2
Insufficient

Ans E

luc2r4, can you explain what you don't understand about Ron's explanation? That will help us to make sure we address whatever the problem is.

Note: you might be making a bad assumption. When the statement says "$10 is enough to buy 11 notepads" that only tells us that we can buy at least 11 notepads for our $10. It doesn't also mean that we can buy at most 11 notepads for $10. I might also be able to buy 20 notepads for $10.

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Can this be solved by combining the "if" inequality with the "?" inequality?

5x + 3y <= 10 (if)
4x + 4y <= 10 (?)
subtract second from first to yield new "?" inequality:
x <= 0 ?

(stmt 1)
x < 1 , not sufficient because we want x <= 0

(stmt 2)
11x <= 10
x <= 10/11, not sufficient because we want x <= 0

(stmt 1 + 2)
x < 1 and x < 10/11
means x < 10/11, not sufficient because we want x <=0

Therefore, answer is E.

Please provide feedback on the logic of my method. In data sufficiency, is it possible to combine an "if" equation, inequality, or value with a "?" equation, inequality, or value?

alok2,

I don't think that you can quite make that jump to have x <= 0 because then your 'y' term goes away instead of becoming a '- y'.

alok2,
gregoryssmith is right--you have completely eliminated y in your result, but if you subtract one from the other you will still have -y.

Ron's method is the most efficient way to attack the problem; please let us know if you have more specific questions.

Thank you,

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Jamie Nelson
ManhattanGMAT Instructor