The only gift certificates that a certain store sold : GMAT Data Sufficiency (DS)
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# The only gift certificates that a certain store sold

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25 Jun 2012, 01:58
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95% (hard)

Question Stats:

48% (02:56) correct 52% (01:41) wrong based on 688 sessions

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The only gift certificates that a certain store sold yesterday were worth either $100 each or$10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday? (1) The gift certificates sold by the store yesterday were worth a total of between$1,650 and $1,800. (2) Yesterday the store sold more than 15 gift certificates worth$100 each.

Diagnostic Test
Question: 30
Page: 25
Difficulty: 600
[Reveal] Spoiler: OA

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25 Jun 2012, 01:59
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SOLUTION

The only gift certificates that a certain store sold yesterday were worth either $100 each or$10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday? Say the number of$100 certificates sold was $$x$$, then the number of $10 certificates sold was $$20-x$$. (1) The gift certificates sold by the store yesterday were worth a total of between$1,650 and $1,800 --> $$1,650<100x+10(20-x)<1,800$$ --> $$1,650<90x+200<1,800$$ --> $$1,450<90x<1,600$$ --> $$145<9x<160$$ --> $$16.1<x<17.8$$. Since $$x$$ is an integer then $$x=17$$. Sufficient. (2) Yesterday the store sold more than 15 gift certificates worth$100 each --> x>15. Clearly insufficient.

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25 Jun 2012, 07:57
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Hi,

Difficulty level: 650

Let's say,
Number of gift certificates worth $100 = x Number of gift certificates worth$10 = y
and x+y=20

Using (1),
$$1650<100x+10y<1800$$
or $$165<10x+y<180$$
or $$165<20+9x<180$$ (given, x+y=20)
or $$145<9x<160$$
or $$145/9<x<160/9$$
or $$16.1< x < 17.7$$
Thus, x = 17. Sufficient.

Using (2),
x > 15. Insufficient.

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25 Jun 2012, 17:46
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(1) The gift certificates sold by the store yesterday were worth a total of between $1 ,650 and$1,800.

Suff as only one combination of $100 and$10 GC is possible for total ranging from 1650-1800 i.e 17 ($100) and 3 ($10) total 1730, all other combinations within this range do not meet total number of GC condition

Number of gift certificates worth $10 = y and x+y=20 Statement (1) 1650 < x+y < 1800 This gives us only one possible solution... 1730 Since there has to be 20 gift certificates and x=100$ and y=10$, 1730 is the only number that is between 1650 and 1800 that corresponds with 20 gift certificates Every other solution is out of range e.g. 16 x 100$ + 4 x 10$= 1640$ or 18 x 100$+ 2 x 10$ = 1820$, both out of the range 1650 < x+y < 1800 Statement (2) clearly insufficient since you can have more than one possible solution. _________________ Kudos if you like the post! Failing to plan is planning to fail. Manager Joined: 02 Jun 2011 Posts: 159 Followers: 1 Kudos [?]: 75 [0], given: 11 Re: The only gift certificates that a certain store sold [#permalink] ### Show Tags 26 Jun 2012, 13:52 x+y = 20 st1.) 1650<100x+10y<1800 with ths eqn and x+y = 20 sufficient st.2) x>15 not sufficient Answer A. Math Expert Joined: 02 Sep 2009 Posts: 36552 Followers: 7078 Kudos [?]: 93156 [0], given: 10553 Re: The only gift certificates that a certain store sold [#permalink] ### Show Tags 29 Jun 2012, 03:10 SOLUTION The only gift certificates that a certain store sold yesterday were worth either$100 each or $10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth$10 each did the store sell yesterday?

Say the number of $100 certificates sold was $$x$$, then the number of$10 certificates sold was $$20-x$$.

(1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and$1,800 --> $$1,650<100x+10(20-x)<1,800$$ --> $$1,650<90x+200<1,800$$ --> $$1,450<90x<1,600$$ --> $$145<9x<160$$ --> $$16.1<x<17.8$$. Since $$x$$ is an integer then $$x=17$$. Sufficient.

(2) Yesterday the store sold more than 15 gift certificates worth \$100 each --> x>15. Clearly insufficient.

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25 Dec 2012, 00:35
Is this a trap question?

That is the intentions of the writer is to make you think that you need 1 and 2 to be able to get the correct answer.

because 2 is obviously not correct and if you weren't able to do 1 properly, you would have to automatically assume that 2 is required.

It seems like it is always advantageous to simply pick the A (or whatever is the harder stem) in these types of questions.
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28 Dec 2012, 17:50
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Yes, this question pretty much wants you to understand that A alone is sufficient, otherwise the fallback answer would be C. St II is obviously not sufficient by itself.
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06 Jul 2014, 02:46
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18 Jul 2015, 21:04
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Hello from the GMAT Club BumpBot!

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27 Mar 2016, 18:58
Here is a visual that should help.

Nearly every GMAT question can be solved by algebra, plugging in numbers, both, or a combination of both. If you have time, then it's best to try both.

This particular method is a hybrid of the two: use algebra to get closer to conceptual understanding, then plug in numbers to test.
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Screen Shot 2016-03-27 at 7.59.24 PM.png [ 125.32 KiB | Viewed 2457 times ]

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The only gift certificates that a certain store sold   [#permalink] 27 Mar 2016, 18:58
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