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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
The only gift certificates that a certain store sold  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 53% (02:11) correct 47% (02:13) wrong based on 1497 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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: The only gift certificates that a certain store sold  [#permalink]

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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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Current Student B
Joined: 29 Mar 2012
Posts: 295
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: The only gift certificates that a certain store sold  [#permalink]

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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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Intern  Joined: 29 Apr 2012
Posts: 1
Re: The only gift certificates that a certain store sold  [#permalink]

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1
(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

100$= 20-x 100(20-x) + 10x = total sales 2000-90x = TS 1) 1650<TS<1800 1650<2000-90x -350<-90x 350>90x x<3.something and 2000-90x<1800 -90x<-200 90x>200 x> 2.something => x=3 DEFINITE x=3 2) 20-x>15 x<5 1,2,3,4 => insufficient A is the answer _________________ Give Kudos for correct answer and/or if you like the solution. Intern  B Status: Don't watch the clock,Do what it does, Keep Going. Joined: 10 Jan 2017 Posts: 37 The only gift certificates that a certain store sold [#permalink] Show Tags 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 Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2815 Re: The only gift certificates that a certain store sold [#permalink] Show Tags 1 Bunuel wrote: 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. We can let h = the number$100 gift certificates sold and t = the number of $10 gift certificates sold. Thus, we have h + t = 20, and we need to determine the value of t. Statement One Alone: The gift certificates sold by the store yesterday were worth a total of between$1650 and $1800. We see that number of$100 gift certificates sold is no more than 17. That is, h ≤ 17.

If h = 17, then t = 3, and the total value of the gift certificates is 17(100) + 10(3) = $1730, which is between$1650 and $1800. If h = 16, then t = 4, and the total value of the gift certificates is 16(100) + 10(4) =$1640. However, this is between not $1650 and$1800. Also, we don’t have to go any further down for the value of h, since we can see that from this point that there is no way the total value is between $1650 and$1800.

Therefore, we see that h must be 17 and t must be 3. Statement one alone is sufficient to answer the question.

Statement Two Alone:

Yesterday the store sold more than 15 gift certificates worth $100 each. We see that h > 15, so h could be 16, 17, 18, 19 or 20 and t could be 4, 3, 2, 1, or 0, respectively. Since we don’t have a unique value for t, statement two alone is sufficient to answer the question. Answer: A _________________ Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Manager  G Joined: 19 Apr 2017 Posts: 170 Concentration: General Management, Sustainability Schools: ESSEC '22 GPA: 3.9 WE: Operations (Hospitality and Tourism) Re: The only gift certificates that a certain store sold [#permalink] Show Tags 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.
It has to be a total of 20 Gift Certificates
16 *100 + 4*10 = 1610 <1650 does not satisfies statement 1
17*100+3*10 = 1710 >1650 and <1800 satisfies statement 1
18*100+2*10= 1810>1800 does not satisfies statement 1

(2) Yesterday the store sold more than 15 gift Certificates worth $100 each. means number of$100 dollar certificates could be 16,17,18,19,20 different values of 100 could give different values of $10 SVP  P Joined: 03 Jun 2019 Posts: 1756 Location: India Re: The only gift certificates that a certain store sold [#permalink] Show Tags Bunuel wrote: 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 Given: The only gift certificates that a certain store sold yesterday were worth either$100 each or $10 each. Asked: If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth$10 each did the store sell yesterday?

Let the number of gift certificates for $10 &$100 be t & h respectively.
t + h = 20 ; h = 20 - t (1)
Q. t=?

(1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and$1,800.
$1650< 10t + 100(20-t) <$1800
1650 = 2000 - 90t < 1800
200<90t<350
2< 20/9< t <35/9 < 4
2 < t < 4
t = 3
3 gift certificates worth $10 each did the store sell yesterday SUFFICIENT (2) Yesterday the store sold more than 15 gift certificates worth$100 each.
h> 15
20 -t > 15
t < 5
t = {1,2,3,4}
NOT SUFFICIENT

IMO A
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