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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

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.

Re: The only gift certificates that a certain store sold [#permalink]

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25 Jun 2012, 08:57

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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.

Re: The only gift certificates that a certain store sold [#permalink]

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25 Jun 2012, 18:46

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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

(2) Yesterday the store sold more than 15 gift certificates worth $100 each

Insuff as more than 15 can mean 16 and 4, 17 and 3, 18 and 2

Re: The only gift certificates that a certain store sold [#permalink]

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26 Jun 2012, 00:30

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Hi,

Difficulty level: 600

Number of gift certificates worth $100 = x 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.
_________________

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.

Re: The only gift certificates that a certain store sold [#permalink]

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28 Dec 2012, 18:50

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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.

Re: The only gift certificates that a certain store sold [#permalink]

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06 Jul 2014, 03:46

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Re: The only gift certificates that a certain store sold [#permalink]

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18 Jul 2015, 22:04

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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The only gift certificates that a certain store sold [#permalink]

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27 Mar 2016, 19:58

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.

Attachments

Screen Shot 2016-03-27 at 7.59.24 PM.png [ 125.32 KiB | Viewed 3079 times ]

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