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

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Asifpirlo
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The three digits of a number add up to 11. The number is div [#permalink] New post   Updated on: 21 Aug 2013, 01:39
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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
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A

Originally posted by Asifpirlo on 21 Aug 2013, 01:36.
Last edited by Bunuel on 21 Aug 2013, 01:39, 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, 01:44
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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, 02:07
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, 02:17
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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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The three digits of a number add up to 11. The number is div [#permalink] New post   Updated on: 11 Jan 2015, 23:24
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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

Originally posted by pacifist85 on 11 Jan 2015, 07:38.
Last edited by pacifist85 on 11 Jan 2015, 23:24, 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, 08:47
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
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Re: The three digits of a number add up to 11. The number is div [#permalink] New post   11 Apr 2018, 20:29
Expert Reply
Hi All,

When a question has a limited number of possibilities, you can sometimes "brute-force" your way to the solution.

Here, we have a bunch of facts to work with:
1) A 3-digit number
2) Digits add up to 11
3) Number is evenly divisible by 5 (so it ends in 0 or 5)
4) The first digit is double the second digit.

Starting with the last fact, we only have a four options:
21_
42_
63_
84_

If you plug 0 in for the last digit, you WON'T end up with a sum of 11, so the last digit MUST be a 5 and the only possible 3-digt number is...

425

Now, answer the question...

Final Answer:
Show Spoiler
A


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Re: The three digits of a number add up to 11. The number is div [#permalink] New post   06 Nov 2019, 19:25
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Re: The three digits of a number add up to 11. The number is div [#permalink]
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