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In the multiplication above, each letter stands for a differ [#permalink]
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Updated on: 20 Oct 2013, 03:58
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AB x CA  DEBC In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit number AB? (A) 23 (B) 24 (C) 25 (D) 32 (E) 42
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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 twodigit number AB? [#permalink]
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19 Oct 2013, 20:32
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.
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Re: What is the twodigit number AB? [#permalink]
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19 Oct 2013, 22:11
irda wrote: AB x CA  DEBC
In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit 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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Re: In the multiplication above, each letter stands for a differ [#permalink]
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20 Oct 2013, 10:09
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.



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Re: What is the twodigit number AB? [#permalink]
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04 Nov 2013, 14:22
Narenn wrote: irda wrote: AB x CA  DEBC
In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit 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?



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Re: In the multiplication above, each letter stands for a differ [#permalink]
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30 Aug 2014, 06:56
AB x CA  DEBC
In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit 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)



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Re: In the multiplication above, each letter stands for a differ [#permalink]
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06 Mar 2016, 20:05
irda wrote: AB x CA  DEBC
In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit 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..



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Re: In the multiplication above, each letter stands for a differ [#permalink]
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07 Mar 2016, 09:53



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Re: In the multiplication above, each letter stands for a differ [#permalink]
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07 Mar 2016, 10:22
irda wrote: AB x CA  DEBC
In the multiplication above, each letter stands for a different nonzero digit, with A x B < 10. What is the twodigit 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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Re: In the multiplication above, each letter stands for a differ [#permalink]
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01 Aug 2017, 11:34
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