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Intern  Joined: 17 Dec 2012
Posts: 26
In the multiplication above, each letter stands for a differ  [#permalink]

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12 00:00

Difficulty:   75% (hard)

Question Stats: 64% (03:00) correct 36% (02:55) wrong based on 269 sessions

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AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

Originally posted by irda on 19 Oct 2013, 14:25.
Last edited by Bunuel on 20 Oct 2013, 03:58, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the two-digit number AB?  [#permalink]

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6
1
First check in answer choices which option does not satisfy. A*B=10
C option does not satisfy. So C cant be the answer.

Now we are left with 23,24,32,42 choices.

Lets check each of them AB*CA = DEBC
IF AB = 23
23
*C2
DEBC
As per this expression C is 6.
23*62=1426 (in answer choice B is 2 while B was 3 in AB.)

So wrong choice.

IF AB = 32
32
*C3
DEBC
As per this expression C is 6.
32*63=1016 (we can straight away reject is as it gives zero as he answer.)

So wrong choice.

IF AB = 24
24
*C2
DEBC
As per this expression C is 8.
24*84=1968 (in answer choice B is 6 while B was 4 in AB.)

So wrong choice.

IF AB = 42
42
*C4
DEBC
As per this expression C is 8.
42*84=3528 (in answer choice B is 2 while B was 2 in AB.)

So right choice.  1 Kudos is you like my Post/Explanation.

Thanks,
AB
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Joined: 22 Feb 2012
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Re: What is the two-digit number AB?  [#permalink]

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2
irda wrote:
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

Show your best approach

A two digit number multiplied by another two digit number creating a 4 digit number. if we maximize one number to 99, we would realize that minimum value of another number would be atleast 11. (because 11*99 = 999). Further more A*B < 10
So we can list down the possible numbers.
13, 14, 15, 16, 17, 18, 19
20, 21, 22, 23, 24
30, 31, 32, 33
40, 41, 42
50, 51
60, 61
...

Now if we look at the options we would realize that only 23, 24, 32, 42 are in the options. So we can eliminate all other cases. Furthermore option C (25) is not in our list, so we can eliminate option C

Here we should understand that when AB is multiplied by CA, units digit is C which is also the value of A*B.

23 :- A = 2, B = 3, C = 6 (23*62) = --26 --------> Tens digit of four digit number (i.e.2) is not the same as B, Eliminate
32 :- A = 3, B = 2, C = 6 (32*63) = --16 --------> Tens digit of four digit number (i.e.1) is not the same as B, Eliminate
24 :- A = 2, B = 4, C = 8 (24*82) = --68 --------> Tens digit of four digit number (i.e.6) is not the same as B, Eliminate
42 :- A = 4, B = 2, C = 8 (42*84) = --28 --------> Tens digit of four digit number (i.e.6) is same as B, Bingo.. GO for Choice E
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Intern  Joined: 15 Dec 2007
Posts: 12
Re: In the multiplication above, each letter stands for a differ  [#permalink]

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1
AB
x CA
---------
DEBC

The fastest way is to look at answers. 2*5=10 means it doesnt work. We're left with 2*3, 2*4,3*2 and 4*2. Start those kinds of questions from E.
42 * C4 > gives us unit digit (C) of DEBC, which is 2*4=8 (B*A=C). Knowing C we know entire AB*CA = 42*84=3528. Check, if B in DEBC=B in AB. Turns out it is. Check other answers, they will prove that answer is E.
Senior Manager  Joined: 08 Apr 2012
Posts: 327
Re: What is the two-digit number AB?  [#permalink]

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Narenn wrote:
irda wrote:
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

Show your best approach

A two digit number multiplied by another two digit number creating a 4 digit number. if we maximize one number to 99, we would realize that minimum value of another number would be atleast 11. (because 11*99 = 999). Further more A*B < 10
So we can list down the possible numbers.
13, 14, 15, 16, 17, 18, 19
20, 21, 22, 23, 24
30, 31, 32, 33
40, 41, 42
50, 51
60, 61
...

Now if we look at the options we would realize that only 23, 24, 32, 42 are in the options. So we can eliminate all other cases. Furthermore option C (25) is not in our list, so we can eliminate option C

Here we should understand that when AB is multiplied by CA, units digit is C which is also the value of A*B.

23 :- A = 2, B = 3, C = 6 (23*62) = --26 --------> Tens digit of four digit number (i.e.2) is not the same as B, Eliminate
32 :- A = 3, B = 2, C = 6 (32*63) = --16 --------> Tens digit of four digit number (i.e.1) is not the same as B, Eliminate
24 :- A = 2, B = 4, C = 8 (24*82) = --68 --------> Tens digit of four digit number (i.e.6) is not the same as B, Eliminate
42 :- A = 4, B = 2, C = 8 (42*84) = --28 --------> Tens digit of four digit number (i.e.6) is same as B, Bingo.. GO for Choice E

How did you know to start plugging in numbers and not try and solve this through theory?
Manager  Joined: 04 Oct 2013
Posts: 150
Location: India
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Re: In the multiplication above, each letter stands for a differ  [#permalink]

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1
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

Given that A x B < 10, the possible values of AB are 23, 32, 24 and 42.

It is also given that A * B = C and units digit of (A* A + C * B) = B

Since, A = 4 and B =2 only satisfies above condition, hence AB =42.

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GMAT 1: 650 Q49 V30 GPA: 3.92
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Re: In the multiplication above, each letter stands for a differ  [#permalink]

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irda wrote:
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

I started first with: 30x30 = 900...so to be 4 digit number, the two numbers must be >30...
A - 23*32 - well..definitely less than 900. so out
B = 24*X2 = 8 so X must be 8..but if we check further, B is not what we need. so out
C = 25*X2 = C=0, but C can't be 0 so out
D = 32*X3 = 6, so C=6, but 32*63 = gives different values for B so out
only E remains..
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: In the multiplication above, each letter stands for a differ  [#permalink]

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irda wrote:
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

Check other Addition/Subtraction/Multiplication Tables problems from our Special Questions Directory
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Math Expert V
Joined: 02 Aug 2009
Posts: 7959
Re: In the multiplication above, each letter stands for a differ  [#permalink]

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irda wrote:
AB
x CA
---------
DEBC

In the multiplication above, each letter stands for a different non-zero digit, with A x B < 10. What is the two-digit number AB?

(A) 23
(B) 24
(C) 25
(D) 32
(E) 42

HI,
I would solve it following way--

first A*B<10 means choice C is out ..
Also from multiplication table above A*B=C...
so looking at the choices digit C= 2*3=6 or 2*4=8..

Checking for the HUNDREDS digit in DEBC..
UNITS digit of A*A + B*C=B..
say C is 6, means either A or B is odd..

1)say A is ODD and B is EVEN....
so A*A + B*C=B..means O*O+E*E=O, but it should be same as B, which is E, so out

2)say A is E and B is O..
so A*A + B*C=B..means E*E+O*E=E, but it should be same as B, which is O, so out..

what rae we left with -- C as 8
so AB =24 or 42..

now we know thereare two possiblitie
1) A=2, B=4, C=8..
A*A + B*C=B
2*2+4*8=4+32=36...
but we should get units digit as B or 6.. not correct

2) A=4, B=2, C=8..
A*A + B*C=B
4*4+2*8=32=...
we get units digit as B or 2.. so correct

ans 42
E

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Joined: 27 Nov 2018
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Re: In the multiplication above, each letter stands for a differ  [#permalink]

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Pretty good explanation for this problem on Yahoo answers: https://answers.yahoo.com/question/inde ... 320AAxf6Ve Re: In the multiplication above, each letter stands for a differ   [#permalink] 02 Feb 2019, 08:28
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