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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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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.
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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
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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
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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] New post 15 Nov 2014, 05:32
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The three digits of a number add up to 11. The number is div [#permalink] New post 11 Jan 2015, 06:38
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Since the sum is 11, it is really easy to try some values.

The last one is 0 or 5.
The first one is twice the second one.

So,
First one: 2
Second one: 1
Third one: 8, doesn't work

First one: 3
Second one: 6
Third one: 2, doesn't work

First one: 4
Second one: 2
Thirdd one: 5, works

There is no way you can have 0 as the last digit, because you cannot have anything more than 4 as the first digit.

So, 4*2*5 = 40 ANS A

Last edited by pacifist85 on 11 Jan 2015, 22:24, edited 1 time in total.
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Re: The three digits of a number add up to 11. The number is div [#permalink] New post 11 Jan 2015, 07:47
We can also solve this by estimating the answer with the help of answer choices if we can't figure out the correct way which Bunuel and others already suggested....

It is a 3 digit no. say abc and divisible by 5 so C has to be either 0 or 5.
Now a=2b so number can be written as 2b*b*0 or 2b*b*5. In either case the last digit of the number will be 0 because 0 multiplied by anything gives 0 and 5*2*anything will also give last digit 0.
There is only one answer with last digit as 0 which is A.


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
Re: The three digits of a number add up to 11. The number is div   [#permalink] 11 Jan 2015, 07:47
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