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# At a certain bookstore, each notepad costs x dollars and

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01 Nov 2010, 22:19
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Difficulty:

95% (hard)

Question Stats:

52% (01:13) correct 48% (01:30) wrong based on 351 sessions

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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?

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

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01 Nov 2010, 22:36
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metallicafan wrote:
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?

1). each notepad cost less than $1 2).$10 is enough to buy 11 notepads

Given: $$5x+3y\leq{10}$$. Question: is $$4x+4y\leq{10}$$?

Note that both statements are telling us basically the same thing:
(1) $$x<1$$;
(2) $$11x<10$$ --> $$x<\frac{10}{11}\approx{0.9}$$;

Now, if both notepad and marker cost very cheap then the answer would be YES but if notepad costs $0.1 and marker costs$3 then the answer would be NO. Not sufficient.

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02 Nov 2010, 18:34
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metallicafan wrote:
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?

1). each notepad cost less than $1 2).$10 is enough to buy 11 notepads

Given: 5x + 3y <= 10 .... (I)
Question: Is 4x + 4y <=10 ?....(II)

Statement (1) x < 1.
If x is a little less than 1 but almost 1, then 5x is little less than 5. Putting in (I) above, we get that y is less than $$\frac{5}{3}$$.
Now we need to put these values in equation (II) and check.
4x will be a little less than 4 and 4y will be less than 4x$$\frac{5}{3}$$ i.e. 6.66. Together, 4x + 4y will be less than 10.66. It may be less than 10 or a little more than 10, hence this is not sufficient.

Statement (2) x < $$\frac{10}{11}$$
If x is a little less than 10/11 but almost 10/11, then 5x is little less than 50/11. Putting in (I) above, we get that y is less than $$\frac{20}{11}$$.
Now we need to put these values in equation (II) and check.
4x will be a little less than 40/11 and 4y will be less than 4x$$\frac{20}{11}$$ i.e. $$\frac{80}{11}$$. Together, 4x + 4y will be less than 120/11 i.e. less than 10.9. It may be less than 10 or more, we do not know, hence this is not sufficient.

Note: You didn't actually need to calculate the data in the second statement. This is because, if we compare 5x + 3y with 4x + 4y, the x term has reduced but the y term has increased. If x is as great as possible, it will keep y small and the extra y in second statement may not matter. We tried with x a little less than 1 in first statement. In second statement, x is smaller than 10/11. Hence, if first statement was not sufficient, no way could the second statement be sufficient.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 30 Aug 2010 Posts: 89 Location: Bangalore, India Re: Notepads and markers [#permalink] ### Show Tags 01 Feb 2011, 23:35 2 metallicafan wrote: 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? 1). each notepad cost less than$1

2). $10 is enough to buy 11 notepads Let me put it in this way: given : $$5x+3y <= 10$$ asking: is $$4x+4y <= 10$$ 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 $$1$$ more$$y$$, making $$y$$ to $$4$$ items from $$3$$items, instead of buying $$1$$ $$x$$, making $$x$$ to $$4$$ items from $$5$$ items. Hence, to answer this question, all we need to know is 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't I?

stmnt1: $$x < 1$$. who cares. i need to know $$is Y < X$$..Not suff.
stmnt2: 11x<10. ==> x<1. Same as above...Not suff.
stmnts 1 & 2. Both are bread slices. Can not make the sandwich with out the extra stuff....Not suff.

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Re: At a certain bookstore, each notepad costs x dollars and [#permalink]

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06 Oct 2013, 03:08
can someone explain why "If $10 is enough to buy 5 notepads and 3 markers" => the translation can't be 5x+ 3y = 10 ( what's wrong with this) and why is it => 5x+3y < = 10 _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Director Joined: 14 Dec 2012 Posts: 810 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Re: At a certain bookstore, each notepad costs x dollars and [#permalink] ### Show Tags 06 Oct 2013, 03:20 1 fozzzy wrote: can someone explain why "If$10 is enough to buy 5 notepads and 3 markers" => the translation can't be 5x+ 3y = 10 ( what's wrong with this)

and why is it => 5x+3y < = 10

LET SAY X= 1 Y =1
THEN 5X + 3Y = 8
STILL 10 DOLLAR IS enough TO BUY 5 NOTEPADS AND 3 MARKERS.

so question wants to say that price of 5 notepads and 3 markers is less than or equal to 10 $hope it is clear. _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8100 Location: Pune, India Re: At a certain bookstore, each notepad costs x dollars and [#permalink] ### Show Tags 06 Oct 2013, 20:19 2 1 fozzzy wrote: can someone explain why "If$10 is enough to buy 5 notepads and 3 markers" => the translation can't be 5x+ 3y = 10 ( what's wrong with this)

and why is it => 5x+3y < = 10

'is enough' means that it suffices. Whether it suffices perfectly or something is leftover is not specified. e.g. it is correct to say $10 is enough to buy the chocolate bar I want. The bar could cost$5 or $8 or$9.2 or $10 etc. I any case,$10 is enough.

Check out a detailed discussion of this question here: http://www.veritasprep.com/blog/2013/09 ... -of-words/
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Re: At a certain bookstore, each notepad costs x dollars and [#permalink]

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18 Jan 2016, 02:39
I am pretty sure this wasnt intended to be a hard question.
Both statements in a way give the same info. So answer should be either D or E.
Since both x and y have changed in the question (4x+4y≤10?) from the given (5x+3y≤10) the answer has to be E
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Re: At a certain bookstore, each notepad costs x dollars and [#permalink]

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20 Feb 2017, 10:54
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Re: At a certain bookstore, each notepad costs x dollars and   [#permalink] 20 Feb 2017, 10:54
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