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Senior Manager  Joined: 25 Nov 2006
Posts: 315
Schools: St Gallen, Cambridge, HEC Montreal
The product of the two-digit numbers above is the three-digi  [#permalink]

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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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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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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
CIO  Joined: 09 Mar 2003
Posts: 413
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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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.
Senior Manager  S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 421
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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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

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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Senior Manager  Joined: 03 Mar 2010
Posts: 348
Schools: Simon '16 (M\$)
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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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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Director  Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 854
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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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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Joined: 16 Nov 2010
Posts: 1252
Location: United States (IN)
Concentration: Strategy, Technology
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: The product of the two-digit numbers above is the three-digi  [#permalink]

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