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The three digits of a number add up to 11. The number is div

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The three digits of a number add up to 11. The number is div [#permalink] New post 21 Aug 2013, 00:36
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B
C
D
E

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Question Stats:

85% (02:14) correct 15% (01:14) wrong based on 40 sessions
The three digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?

A. 40
B. 72
C. 78
D. 88
E. 125
[Reveal] Spoiler: OA

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Last edited by Bunuel on 21 Aug 2013, 00:39, edited 1 time in total.
Edited the question.
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Re: The three digits of a number add up to 11. The number is div [#permalink] New post 21 Aug 2013, 00:44
Expert's post
Asifpirlo wrote:
The three digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?

A. 40
B. 72
C. 78
D. 88
E. 125


As the number is divisible by 5, the product of the three digits must be divisible by 5. Only A and E subscribe to that.
Now, it is very easy to see that 40 = 5*8 = 5*4*2 and 5+4+2=11.
A.

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Re: The three digits of a number add up to 11. The number is div [#permalink] New post 21 Aug 2013, 01:07
Asifpirlo wrote:
The three digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
A. 40
B. 72
C. 78
D. 88
E. 125


xyz is a three digit integer divisible by 5. So z can take only 0 or 5. We are also given that x = 2y
This means x+y (2y+y) must be a multiple of 3

xy5 or xy0
CASE 1
x+y+0 = 11
x+y=11
This can't be the case because 11 is not a multiple of 3

CASE 2
x+y+5 = 11
x+y=6
solving we get, x=4 & y=2
So the 3 digit number is 425
Thus the product of the digits will be = 4 x 2 x 5 = 40
Answer A

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Re: The three digits of a number add up to 11. The number is div [#permalink] New post 21 Aug 2013, 01:17
Expert's post
Asifpirlo wrote:
The three digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?

A. 40
B. 72
C. 78
D. 88
E. 125


Say the three-digit number is abc.

The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 11 --> a+b+c=11

So, either a+b+c=2b+b+0=11 or a+b+c=2b+b+5=11. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=2 --> a=4 and c=5 --> a*b*c=40.

Answer: A.

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Re: The three digits of a number add up to 11. The number is div   [#permalink] 21 Aug 2013, 01:17
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