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# Randall purchased a shirt for $19.44 using a$20 bill. If his correct

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Math Expert
Joined: 02 Sep 2009
Posts: 50010
Randall purchased a shirt for $19.44 using a$20 bill. If his correct  [#permalink]

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09 Jun 2018, 00:13
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Difficulty:

(N/A)

Question Stats:

67% (02:08) correct 33% (01:27) wrong based on 34 sessions

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Randall purchased a shirt for $19.44 using a$20 bill. If his correct change was returned in only dimes ($0.10) and pennies ($0.01), how many coins could Randall have received?

(A) 9
(B) 21
(C) 29
(D) 37
(E) 44

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Joined: 11 Apr 2018
Posts: 120
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Randall purchased a shirt for $19.44 using a$20 bill. If his correct  [#permalink]

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09 Jun 2018, 01:20
Amount to be retuned = $0.56 = 56 Cents. 1 Dime =$0.10 = 10 Cents.
1 Penny = $0.01 = 1 Cent. Consider X Dimes and Y Pennies are given back. Then, equation can be formed as 10X + 1Y = 56. Possible values of (X,Y) pairs are (0,56 ), (1,46), (2,36), (3,26), (4,16), (5,6). So, number of coins received could be 56, 47, 38, 29, 20, 11. Only 29 is among the options. So, C is the correct answer. CEO Joined: 08 Jul 2010 Posts: 2564 Location: India GMAT: INSIGHT WE: Education (Education) Re: Randall purchased a shirt for$19.44 using a $20 bill. If his correct [#permalink] ### Show Tags 09 Jun 2018, 01:22 1 Bunuel wrote: Randall purchased a shirt for$19.44 using a $20 bill. If his correct change was returned in only dimes ($0.10) and pennies ($0.01), how many coins could Randall have received? (A) 9 (B) 21 (C) 29 (D) 37 (E) 44 His return = 20 - 19.44 =$0.56

now 0.1 x + 0.01 y = 0.56

i.e. 10x + y = 56

i.e. (x, y) = (5, 6) or (4, 16) or (3, 26) etc.

i.e. x+y = 11 or 20 or 29

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Intern
Joined: 27 Apr 2015
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Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
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Re: Randall purchased a shirt for $19.44 using a$20 bill. If his correct  [#permalink]

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09 Jun 2018, 07:41
Change due = $0.56 If A denotes every$0.10 and B denotes every $0.01, then Possible combinations using (A)$0.10 and (B) $0.01 are as follows: 1A + 46B --> total 47 coins 2A + 36B --> total 38 coins 3A + 26B --> total 29 coins --> Correct answer! Director Joined: 14 Dec 2017 Posts: 503 Re: Randall purchased a shirt for$19.44 using a $20 bill. If his correct [#permalink] ### Show Tags 09 Jun 2018, 08:38 Bunuel wrote: Randall purchased a shirt for$19.44 using a $20 bill. If his correct change was returned in only dimes ($0.10) and pennies ($0.01), how many coins could Randall have received? (A) 9 (B) 21 (C) 29 (D) 37 (E) 44 Randall received a change of$0.56.

Let $$d$$ be the # of dimes & $$p$$ be the # of pennies Randall got in return.

Hence we have, $$0.10d + 0.01p = 0.56$$

Multiplying by 100 on both sides, we get

$$10d + p = 56$$, hence (d,p), that satisfy the equation are (1,46), (2,36), (3,26), (4,16), (5,6)

# of coins received by Randall can be 47 or 38 or 29 or 20 or 11.

Thanks,
GyM
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Re: Randall purchased a shirt for $19.44 using a$20 bill. If his correct  [#permalink]

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09 Jun 2018, 16:42
D + P = Total Coins
5 + 6 = 9
4 + 16 = 20
3 + 26 = 29 Only Direct Hit on the options

2 + 36 = 37
1 + 46 = 47
0 + 56 = 56
Re: Randall purchased a shirt for $19.44 using a$20 bill. If his correct &nbs [#permalink] 09 Jun 2018, 16:42
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