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The product of the twodigit numbers above is the threedigi
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18 Mar 2014, 01:42
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The Official Guide For GMAT® Quantitative Review, 2ND EditionAB 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 Problem Solving Question: 174 Category: Arithmetic Operations on rational numbers Page: 85 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: The product of the twodigit numbers above is the threedigi
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18 Mar 2014, 01:43
SOLUTIONAB 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.
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Re: The product of the twodigit numbers above is the threedigi
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18 Mar 2014, 03:46
Answer = D = 21 21 (AB) x 12 (BA) = 252 (ACA) All other options do not satisfy In Option A, it comes up as A = B & AB x BA = ABA; so ignore it Option B, C & E do not satisfy Answer = D
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Re: The product of the twodigit numbers above is the threedigi
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25 Mar 2014, 14:13
Bunuel wrote: SOLUTION
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. Why is the units digit not 1? Thanks!



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Re: The product of the twodigit numbers above is the threedigi
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25 Mar 2014, 23:00
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionAB 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 While plugging answer choices is good way to attack this question, it is good to leverage some facts given in the question stem first, so that we need to try out only a few choices. 1) Units digit of AB*BA is A. That means B*A = A, This is possible when B=1. so we have that A1 * 1A = 1C1 2) Since A, B, and C are DIFFERENT nonzero digits and since B=1, we can say that A is not equal to 1 So we have to check only Choice D and E.
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Re: The product of the twodigit numbers above is the threedigi
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23 May 2014, 09:20
I solved it this way: 1) We can eliminate A, C and E > A:11: It's said  Three different nonzero digits, so it can't be 11 > C: Just plug in numbers 13*31= 403 ( It's wrong because 1st and 3rd Digits are the same in the product) > E: Same as c 31*13 = 403 ( It's wrong because 1st and 3rd Digits are the same in the product) So we have just B and D left. 2) If we use the multiplication rules, it is evident that > AB x BA  ACA > So, BxA = A so B must be 1; Answer D  21 is correct
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Re: The product of the twodigit numbers above is the threedigi
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30 Mar 2015, 22:17
NAL9 wrote: Bunuel wrote: SOLUTION
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. Why is the units digit not 1? Thanks! Also am not clear why units digit cannot be 1?



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Re: The product of the twodigit numbers above is the threedigi
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30 Mar 2015, 23:34
TOB2020 wrote: NAL9 wrote: Bunuel wrote: SOLUTION
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. Why is the units digit not 1? Thanks! Also am not clear why units digit cannot be 1? What you need is AB * BA = ACA. You need to find AB. In the product ACA, the unit's digit (A) should be the same as the tens digit of AB (which is also A) i.e. the tens digit of the number you want to find. You know that 12 * 21 = 252 The units digit of 252 is 2. It should be same as the tens digit of the first number i.e. 12 but the tens digit of 12 is 1. So the product should instead be written as 21 * 12 = 252. Now, tens digit of AB (i.e. 21) is 2 and units digit of ACA (252) is also 2. They match. So AB = 21 and not 12. This is what is meant by "units digit is not 1". When you have 12*21, the product's units digit should be the same as the tens digit of 12 so it should be 1. But the product's units digit is not 1; it is 2. Hence, you discard this option.
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Re: The product of the twodigit numbers above is the threedigi
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31 Mar 2015, 12:00
[quote="Bunuel"] SOLUTIONAB 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 We are told that all 3 digits are different. So we can reject option (A). Let us put values and find out the answer. Option (B) 12 So, 12*21. But here units digit is not A i.e.1. So reject this. Option (C) 13 So, 13*31. But here units digit is not A i.e.1. So reject this. Option (D) 21 So, 21*12 = 252 = AB x BA = ACA. This satisfies. Hence option (D).  Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimusprep.com/gmatondemandcourse



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Re: The product of the twodigit numbers above is the threedigi
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31 Mar 2015, 21:38
AB * BA  ACA
A*B<10 means that B=1 and A can be 2,3,4,5,6,7,8,9. Eliminate A,B,C answers
Test only 21 and 31
21*12=252, it fits
D



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Re: The product of the twodigit numbers above is the threedigi
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26 Nov 2016, 02:27
Units digit is A and A*B = A => B=1. Also A,B, and C are different digits. Thus, Discard A, B and C choices.
Upon checking 21 we see that it matches the criteria and is, therefore, the answer choice.



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The product of the twodigit numbers above is the threedigi
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21 Mar 2019, 12:51
Hi, If this was to be done logically, this is how it would be like Lets See how two numbers can be multiplied XY *YX  \(\hspace{3cm}X^2 \hspace{.3cm} XY\) \(\hspace{1.3cm} XY \hspace{1cm} Y^2\hspace{.5cm}\) 0  \(\hspace{1.3cm} X \hspace{1cm} Z \hspace{.7cm}\) X Now here we are given certain Conditions , that X and Y are distinct integers and product of XY < 10 The Units Place of product is obtained when we do the following : X*Y +0 = X what can we infer . Using the identity that 1*A = A we can say that Y is definitely 1. And 1*X =X The Hundreds Place of product is obtained when we do the following : XY + any carry forward from ten's place But . Its told to us that its X . Since we have seen that Y is 1 XY is =X if there is no carry forward from Ten's Place. The Tens Place of product is obtained when we do the following : \(X^{2}\) +\(Y^{2}\) = Z But here we Know that Y =1 So \(X^{2}\) +1 gives us the value of Z. Also Since tens Place is a number <10, because any double digit number would lead to carry forward to hundreds place the only integer whose square is less than 10 is 2,3, But \(2^{2}\)= 4 , \(3^{3}\)=9, If it were 3 then \(3^{2}\) would be 9 and \(Y^{2}\) =1 which would be 10, this would provide carry to hundreds digit. So X is not 3 , hence X is 2. So we have X as 2 and Y as 1 which is 21 Probus
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The product of the twodigit numbers above is the threedigi
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