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Math Expert
Joined: 02 Sep 2009
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In multiplication of the two digit numbers wx and cx, where w, x, and
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11 Apr 2018, 09:09
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42% (03:07) correct 58% (02:42) wrong based on 238 sessions
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In multiplication of the two digit positive numbers wx and cx, where w, x, and c are unique nonzero digits, the product is a three digit number. What is w + c  x? (1) The three digits of the product are all the same and different from w, c and x. (2) x and w + c are odd numbers.
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Joined: 04 Apr 2018
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Re: In multiplication of the two digit numbers wx and cx, where w, x, and
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11 Apr 2018, 09:49
Given : wx*cx = _ _ _ . Asked is w+cx.
(1). If three digits of the product are all the same, then the product has only 9 possibilities which are : (111, 222, 333, 444, .....................,888,999). Now, we already know that 111= 37*3, hence all the possibilities can be rewritten as follows: (3*37 , 6*37 , 9*37 ,.....................,24*37,27*37) Only the last possibility matches the given sets of conditions. Hence 27*37=999, because in this case ten's place is the same digit for both 27 as well as 37. So, w+cx = 2+37 = 4 (Easily deduced). Hence SUFFICIENT !
(2). This mentions that x and w + c are both odd numbers. There are many possibilities. We know only ODD+EVEN=ODD. So,either of (w,c) are (odd,even) or (even,odd). And x =ODD. Case1. Let's say for one possibility, x=1; w=2; c=3 . This also satisfies the inital given condition that multiplication of the two digit numbers gives 3 digited product. Hence, So, w+cx = 2+31 = 4. Case2. Now for another possibility, say x=3; w=1; c=2. This also satisfies the inital given condition that multiplication of the two digit numbers gives 3 digited product. Hence, So, w+cx = 1+23 = 0. (There could be many other cases too but we can conclude from 2 cases only.) So both the case gives a different answer, hence we cannot arrive at a unique solution from (2). Hence INSUFFICIENT !
So, the final answer to the question should be option A.




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Joined: 02 Oct 2017
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Re: In multiplication of the two digit numbers wx and cx, where w, x, and
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22 Apr 2018, 18:33
I) Number could be 111,222,....999 111 has factors as 37*3 222 has 37*6 ... ... 999=37*27 only 999 has same digit in its unit place. Sufficient II) can have multiple combination So answer is A Posted from my mobile device
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Joined: 21 Jun 2017
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Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)

Re: In multiplication of the two digit numbers wx and cx, where w, x, and
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13 Sep 2018, 09:04
Stem: wx and cx product to be commented upon. (10w+x)(10c +x) = 100(wc) + 10wx + x^2 so , this is some number with three digits as wc (w+c)x and x^2 > hundreds tens and units digit. we are asked w+cx 1. all three digits are same. this means (w+c)x = x^2 > x= w+c. Hence, w+cx =0. Sufficient 2. x is odd means, in our number x^2 can only be 1 or 9 > x can be 1 or 3. Ok Units digit done, lets move to tens digit. w+c is odd means, tens digit> odd*1 or odd*3. The relation between w+c and x cannot be determined hence insufficient.
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Joined: 22 Sep 2018
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Re: In multiplication of the two digit numbers wx and cx, where w, x, and
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12 Oct 2018, 04:52
Wait, I found that I can calculate from statement 2. 1). X^2 is an 1d interger and x is odd => x = 1 or x = 3. 2) If x=1 => w+c=1 => impossible bc w is not equal to c. 3). If x=3 => w+c=3. It’s possible bs w and c may be 1 and 2 and vice versa
=> So, x=3 and w+c=3 Then w+cx= 0.
So the answer should be D, right?
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Re: In multiplication of the two digit numbers wx and cx, where w, x, and
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12 Oct 2018, 04:52






