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# The product of the two-digit numbers above is the three-digi

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Joined: 25 Nov 2006
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The product of the two-digit numbers above is the three-digi  [#permalink]

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29 Nov 2007, 11:07
7
00:00

Difficulty:

75% (hard)

Question Stats:

62% (01:15) correct 38% (01:24) wrong based on 256 sessions

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AB
x BA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit number AB?

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-the-two-digit-numbers-above-is-the-three-digi-168914.html
Director
Joined: 09 Jul 2007
Posts: 917
Location: London
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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29 Nov 2007, 12:45
lumone wrote:
AB
x BA
--------
= ACA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit 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.
Intern
Joined: 25 Nov 2007
Posts: 33
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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29 Nov 2007, 17:30
alrussell wrote:
lumone wrote:
AB
x BA
--------
= ACA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit 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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Joined: 09 Mar 2003
Posts: 413
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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29 Nov 2007, 20:14
Ravshonbek wrote:
lumone wrote:
AB
x BA
--------
= ACA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit 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 two-digit numbers above is the three-digi  [#permalink]

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12 May 2011, 11:11
lumone wrote:
AB
x BA
--------
= ACA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit number AB?

(A) 11
(B) 12
(C) 13
(D) 21
(E) 31

12
21
---
252 so, ab=12
and
21
12
---
252 so, ab =21
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Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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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 two-digit numbers above is the three-digi  [#permalink]

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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 two-digit numbers above is the three-digi  [#permalink]

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13 May 2011, 05:08
2
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)

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Joined: 12 Jan 2013
Posts: 142
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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27 Dec 2013, 08:29
lumone wrote:
AB
x BA
--------
= ACA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit 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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Joined: 02 Sep 2009
Posts: 58434
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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02 May 2015, 03:21
3
1
lumone wrote:
AB
x BA

The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-the-two-digit-numbers-above-is-the-three-digi-168914.html
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Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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08 Jan 2019, 16:24
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Re: The product of the two-digit numbers above is the three-digi   [#permalink] 08 Jan 2019, 16:24
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