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

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13 Jun 2011, 10:15
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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.

Official Guide 12 Question

 Question: 30 Page: 25 Difficulty: 750

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Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-only-gift-certificates-that-a-certain-store-sold-134895.html
[Reveal] Spoiler: OA

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13 Jun 2011, 23:29
a number of $100 certificates can be only 17. for 16,$100 the total value < 1650.
for 18,$100 the total value > 1800. thus 17$100 and 3, $10. A sufficient. b since total value is not known, it can be 16,$100 and 4, $10 or 17 and 3, 18 ,2 and 19, 1. Not sufficient. A _________________ Visit -- http://www.sustainable-sphere.com/ Promote Green Business,Sustainable Living and Green Earth !! Intern Joined: 18 Mar 2013 Posts: 1 Followers: 0 Kudos [?]: 1 [1] , given: 2 Re: The only gift certificates that a certain store sold [#permalink] ### Show Tags 25 Aug 2013, 06:05 1 This post received KUDOS Baten80 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. Official Guide 12 Question  Question: 30 Page: 25 Difficulty: 750 Find All Official Guide Questions Video Explanations: I solved this problem as follows : #of$100 tickets = x
# of $10 tickets = y x+y = 20 y=? 1) 100x+10y=1650~1800 here I identified this as a Diophantine equation coz we are dealing with integers... ?? 100x=1650~1800 - 10y x=(1650~1800 - 10y )/100 Now, 10y will be some integer not equal to 0 . the maximum value would be somewhere in the range 1800 - 10y which MUST ALSO be a multiple of 100 . The only integer which satisfies the above equation [ x=(1650~1800 - 10y )/100 ] is 1700 therefore x = 17 Math Expert Joined: 02 Sep 2009 Posts: 36601 Followers: 7097 Kudos [?]: 93477 [2] , given: 10563 Re: The only gift certificates that a certain store sold [#permalink] ### Show Tags 25 Aug 2013, 06:14 2 This post received KUDOS Expert's post 2 This post was BOOKMARKED 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-only-gift-certificates-that-a-certain-store-sold-134895.html
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Re: The only gift certificates that a certain store sold   [#permalink] 25 Aug 2013, 06:14
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# The only gift certificates that a certain store sold

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