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The product of the twodigit numbers above is the threedigi
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29 Nov 2007, 11:07
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62% (01:15) correct 38% (01:24) wrong based on 256 sessions
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AB x BA The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB? (A) 11 (B) 12 (C) 13 (D) 21 (E) 31 OPEN DISCUSSION OF THIS QUESTION IS HERE: theproductofthetwodigitnumbersaboveisthethreedigi168914.html
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Re: The product of the twodigit numbers above is the threedigi
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29 Nov 2007, 12:45
lumone wrote: AB x BA  = ACA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31
for me the easiest method is back solving. start from A D or E. most prob. i would start from E.



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Re: The product of the twodigit numbers above is the threedigi
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29 Nov 2007, 17:30
alrussell wrote: lumone wrote: AB x BA  = ACA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31 11 works. 11 x 11 = 121. Or ACA
It says A B and C are different integer so it can't be 11
It is D



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Re: The product of the twodigit numbers above is the threedigi
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29 Nov 2007, 20:14
Ravshonbek wrote: lumone wrote: AB x BA  = ACA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31 for me the easiest method is back solving. start from A D or E. most prob. i would start from E.
I agree with this (and also the comment above on why 11 is wrong). I'd add one thing:
If
AB
xBA

ACA
Then that means that the units digit of B x A is A. Since the answers show that 1 is clearly an option for A or B, I'd say it's safe that B is 1 and A is something else. So you can eliminate A, B, C and just try D and E.



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Re: The product of the twodigit numbers above is the threedigi
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12 May 2011, 11:11
lumone wrote: AB x BA  = ACA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31 To me 12 and 21 both satisfy the condition. Answer is D (21). Please help 12 21  252 so, ab=12 and 21 12  252 so, ab =21
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Re: The product of the twodigit numbers above is the threedigi
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12 May 2011, 11:21
lumone wrote: AB x BA  = ACA see the form carefully, its ACA ian7777 wrote: [A]1[B]2 21  25[B]2 so, ab=12 in this A=1 BUT IN ACA A=2 so it is 21. [A]2[B]1 12  25[A]2
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Re: The product of the twodigit numbers above is the threedigi
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12 May 2011, 21:17
AB * BA = AB+ B^2+ A^2 + BA
AB = BA = A means B = 1. Hence options D and E prevail.
B^2+A^2 = 2^2 + 1 = 5
D.



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Re: The product of the twodigit numbers above is the threedigi
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13 May 2011, 05:08
11 * 11 = 121 (Not Possible as A B C are different) 12 * 21 = 252 ( A = 2, B = 1, but result is in the form BCB) 13 * 31 = 403 (Not possible) 21 * 12 = 252  Possible 31 * 13 = 403 (Not Possible) Answer  D
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Re: The product of the twodigit numbers above is the threedigi
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27 Dec 2013, 08:29
lumone wrote: AB x BA  = ACA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31 First plot the range of the numbers.. The most efficient way is if you notice the range of the alternatives, they tell you possible values of A,B and thus the range is 1,2,3 for A and B. Also, since none of them can be the same, answer A is eliminated. Now recognize that B*A = A which means that B = 1, this eliminates B and C. Now try the two that are left. Start with 21, you see that 21*12 = 252 and thus D is the correct answer.



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Re: The product of the twodigit numbers above is the threedigi
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02 May 2015, 03:21
lumone wrote: AB x BA
The product of the twodigit numbers above is the threedigit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the twodigit number AB?
(A) 11 (B) 12 (C) 13 (D) 21 (E) 31 First of all, since the digits must be distinct, then we can eliminate option A (11). Next, simply plug in the options and see which satisfies AB x BA = ACA: (B) 12 > 12*21 > the units digit is not 1. Discard. (C) 13 > 13*31 > the units digit is not 1. Discard. (D) 21 > 21*12 = 252 = AB x BA = ACA. Bingo. Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: theproductofthetwodigitnumbersaboveisthethreedigi168914.html
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Re: The product of the twodigit numbers above is the threedigi
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Re: The product of the twodigit numbers above is the threedigi
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