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A children's gift store sells gift certificates in denominations of $3

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A children's gift store sells gift certificates in denominations of $3  [#permalink]

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New post 04 Jan 2019, 12:26
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

43% (00:17) correct 57% (02:43) wrong based on 14 sessions

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A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?

A.5
B. 7
C.6
D.31
E.18
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Re: A children's gift store sells gift certificates in denominations of $3  [#permalink]

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New post 04 Jan 2019, 12:37
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Total $3 certificates sold = m => total value $ 3m
Total $5 certificates sold = n => total value $ 5n
Sum total of all the certificates = $(3m + 5n) = $93 given
=> 3m + 5n = 93
=> n = (93 - 3m)/5

Now n will be integer only when 93 - 3m is an integer multiple of 5 (as denominator is 5)
93 - 3m = 3*31 - 3m = 3(31-m) can be a multiple of 5 only when it's unit's digit is either 5 or 0
for 3*(31-m) to have unit's digit as 5 or 0 => 31-m has to have unit's digit of 5 or 0
so possible values of m are 1, 6, 11, 16,21, 26 (as when m = 31 then 31-m will become 0 -> making n as zero -> non-natural!)
So 6 values

[Alternate way of finding number of terms
1,6,...,26 is an arithmetic sequence whose first term is 1, common difference is 5 and last term is 26
So, total numbers = (26-1)/5 + 1 = 6 terms]

So, Answer is C

Hope it helps!
cfc198 wrote:
A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?

A.5
B. 7
C.6
D.31
E.18

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A children's gift store sells gift certificates in denominations of $3  [#permalink]

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New post 04 Jan 2019, 12:46
cfc198 wrote:
A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?

A.5
B. 7
C.6
D.31
E.18


The answer is 6 (C)

detailed in previous post:
https://gmatclub.com/forum/a-children-s ... 14647.html
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Re: A children's gift store sells gift certificates in denominations of $3  [#permalink]

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New post 05 Jan 2019, 01:29
cfc198 wrote:
A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?

A.5
B. 7
C.6
D.31
E.18


Discussed here: https://gmatclub.com/forum/a-children-s ... fl=similar

TOPIC IS LOCKED AND ARCHIVED.
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Re: A children's gift store sells gift certificates in denominations of $3   [#permalink] 05 Jan 2019, 01:29
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