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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] New post 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.

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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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Re: Gift Certificate [#permalink] New post 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.

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Re: The only gift certificates that a certain store sold [#permalink] New post 25 Aug 2013, 06:05
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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

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Question: 30
Page: 25
Difficulty: 750

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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
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Re: The only gift certificates that a certain store sold [#permalink] New post 25 Aug 2013, 06:14
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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?

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.

Answer: A.

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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