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Manager
Manager
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Joined: 14 Dec 2011
Posts: 65
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
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Kudos [?]: 5 [0], given: 24

GMAT Tests User
What to do? [#permalink] New post 01 Jan 2012, 21:45
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

74% (02:03) correct 26% (01:43) wrong based on 54 sessions
__2A
x__B
____
CC


In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 5, what is the value of C?

6
5
4
3
2

Image


No idea how to solve this, I think I do not understand the question!
[Reveal] Spoiler: OA
Intern
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Re: What to do? [#permalink] New post 02 Jan 2012, 10:08
If A+B=5
assuming A and B are positive then A*B<10 (they could be either 1,2,3,4)
therefore
A*B=C
2*B=C
A+B=5

Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=3 --> C=6
Manager
Manager
avatar
Joined: 14 Dec 2011
Posts: 65
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
Followers: 1

Kudos [?]: 5 [0], given: 24

GMAT Tests User
Re: What to do? [#permalink] New post 03 Jan 2012, 00:21
Does it not say that 2*A*B = C*C?...

how did you come up with:

A*B=C
2*B=C

Cheers!

Can a distinct digit not be 2.5? Or some other number like that?
Intern
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Re: What to do? [#permalink] New post 03 Jan 2012, 02:05
A and B have to be a non-negative integer --> distinct digit
The fact that the question shows you the multiplication in a vertical display gives you a strong hint on how to solve it.
Neither A nor B can be zero --> B=0 then the product is 0, A=0 -->b=5 2A*B=100
Hence A,B are between 1-9
Using a vertical multiplication (which yields the same result as a horizontal multiplication, just a matter of convenience) the product of the factors' unit digits equals to the unit digit of their product.
If the product is lower then 10 then it only has a unit digit.
That is the case here as the sum of the two factors (in this case A+B) equals 5 and they are both<>0.
Therefore A*B=C
For the same reason the tens digit is equal to B*2
Hence 2*B=C
The third equation is given
A+B=5

Hope this helps
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Re: What to do? [#permalink] New post 03 Jan 2012, 02:07
One thing I didn't simplify
A and B are between 1-9. since thier sum is 5 then they are between 1-4
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Re: What to do? [#permalink] New post 03 Jan 2012, 02:12
Expert's post
Impenetrable wrote:
__2A
x__B
____
CC


In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 5, what is the value of C?

6
5
4
3
2

Image


No idea how to solve this, I think I do not understand the question!


The letters are placeholders for some specific digits. You need to plug in digits for the letters such that the multiplication relation holds. Also, a letter stands for the same digit in each occurrence i.e. the product is CC means both the digits of the product are the same.

In such questions, it is sometimes a good idea to look at the overall picture. A two digit number starting with 2 is multiplied by a single digit number to give CC i.e. 00 or 11 or 22 or 33 or 44 or 55 or 66 or 77 or 88 or 99
The only numbers out of these which can be obtained by multiplying 2A by B are 00 (If B = 0 but B and C must be distinct) or 22 (If A = 2 and B = 1 but A, B and C must be distinct), 44 (If A = 2 and B = 2 but again, A, B and C must be distinct) or 66 (If A = 2 and B = 3. Also, A + B = 5 so condition satisfied. This must be the answer.)

The multiplication will look like this:
__22
x__3
____
_66

Answer (A)
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Re: What to do?   [#permalink] 03 Jan 2012, 02:12
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