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

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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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.

How did you know to start plugging in numbers and not try and solve this through theory?

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.

Answer: (E)

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..

Check other Addition/Subtraction/Multiplication Tables problems from our Special Questions Directory
_________________

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

_________________

Pretty good explanation for this problem on Yahoo answers: https://answers.yahoo.com/question/inde ... 320AAxf6Ve

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