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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, 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.

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

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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

(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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25 Jun 2012, 23:30

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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.
_________________

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

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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.

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

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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 the two. 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 6112 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

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

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28 Jun 2017, 06:04

I approached 1 differently than the posts. Hopefully it helps.

(1) Given that 20 gift cards were sold... I saw 1,650 and tried to rationalize how to break that down. I know that I have to sell 16(100)+4(10) which is short of 1,650.

I progressed to 17(100)+3(10)=1,730 which checks out. 18(100)+2(10)=1820 which is outside the scope.

Therefore, I have only 1 possible answer. Sufficient

(2) Knowing nothing about (1), this is not sufficient by itself. So it cannot be B.

Knowing that (1) is sufficient, we no longer need (2). Not Sufficient

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

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24 Jul 2017, 15:56

For these diophantine equations, it is actually possible to reduce the question pretty succinctly with algebra. Some people don't need to do that, and it does take a few extra seconds, but if you're interested this is how I did it.

Given:

100(A) + 10(B) = ? A + B = 20

Statement 1:

100(A) + 10(B) = (1650, 1800) --> divide the whole equation by 10 to simplify. 10(A) + B = (165, 180) --> use the given information to substitute in for A. 10(20-B) + B = (165, 180) 200 - 9B = (165, 180) --> subtract 200 and divide by -1. 9B = (20, 35)

How many multiples of 9 are there between 20 and 35? Only one, so you know that B (which is an integer) can only take one value.

Statement 2:

There is more than one option for A and B, and the overall total is not constrained.

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

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23 Sep 2017, 23:47

i believe this to be one of the "poster boy" questions for the gmat . While solving we should concentrate on the question rather than concentrating on the fact that the time is running out. Here goes the solution. 100x+10y=w and x+y=20

1. 1650<w<1800 x=16 then y=5 so putting this value in the 1st equation. not possible as 1650<w x=17 then y=3 possible x=18 then y=2 not possible as y<1800 2. not sufficient A