In multiplication of the two digit numbers wx and cx, where w, x, and

Question

In multiplication of the two digit positive numbers wx and cx, where w, x, and c are unique non-zero 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.

styxnexus · Accepted Answer

Given :   wx*cx = _ _ _ . Asked is w+c-x.

(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 re-written 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+c-x = 2+3-7 = -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+c-x = 2+3-1 = 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+c-x = 1+2-3 = 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.

ShankSouljaBoi · Answer

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+c-x
1. all three digits are same. this means (w+c)x = x^2 ----> x= w+c. Hence, w+c-x =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.

push12345 · Answer

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

Phanh1909 · Answer

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+c-x= 0.

So the answer should be D, right?

Posted from my mobile device

deadpoo7 · Answer

This a very elegant way of solving this question, tanks ShankSouljaBoi. I'm just reframing your sentences:
we have 2 numbers wx and cx and their product results in a 3 digit number
Solution:
1.lets rewrite wx and cx as (10w+x) and (10c+x) respectively
2. lets multiply the two numbers, wx * cx => (10w+x) * (10c+x)=> 100(wc) + 10x(c+w) + x^2 -> equation 1
3. for 3 digit number abc, its of the form => 100a+10b+c -> equation 2
4. we can compare equation 1 and equation 2
5. coming back to the question and more specifically the first statement, it says that if all the digits in the third equation are equal, then a=b=c => wc=w(c+x)=x2 -> equation 3
6. lets look at the second part in equation 3, x(c+w)=x^2 => w+c=x => w+c-x=0, so we can arrive at the solution
7. for the second statement I agree with what ShankSouljaBoi said, but IMO since we are sure that statement 1 is sufficient to answer the question, I didn't bother looking at statement 2, hence the answer to the solution is A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In multiplication of the two digit numbers wx and cx, where w, x, and

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In multiplication of the two digit numbers wx and cx, where w, x, and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards