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kevincan
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w x . X c x ... _____ In the above mutiplication of the two 19 Aug 2006, 09:01
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....w x

.X c x
... _____



In the above mutiplication of the two digit 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.



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w x . X c x ... _____ In the above mutiplication of the two 19 Aug 2006, 13:52
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kevincan
....w x

.X c x
... _____



In the above mutiplication of the two digit 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.
Show more

its A.

from (1) the only three digit number with all same digits is 999 that has factors with same unit digit.
999 = 27 x 37.
so w+c -x = 2+3-7 = -2.

from (2) if x and w+c are odd numbers, w + c -x is also odd but we do not know the value......
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w x . X c x ... _____ In the above mutiplication of the two 19 Aug 2006, 14:10
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Nicely done- I hope it didn't take too long
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w x . X c x ... _____ In the above mutiplication of the two 19 Aug 2006, 17:27
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yes! 8-). it was so smooth. :cool it took me less than a minuet to solve it. compared with your other questions, this one is a piece of cake.

i say this, in terms of real gmat test standard, is the best question that you ever posted on this forum. your other questions were also great but they were more time consuming and really tough. gmat questions are not tough; they are simply tricky.

thanks for all your efforts........
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w x . X c x ... _____ In the above mutiplication of the two 20 Aug 2006, 01:43
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Professor

from (1) the only three digit number with all same digits is 999 that has factors with same unit digit.
999 = 27 x 37.
so w+c -x = 2+3-7 = -2.

Show more


Proffesor, can you please explain how you obtained 999 ?Did you factorize all the 3 digit numbers having same digits, i.e. 111,222,333,444,555,666,777,888 and 999 ?

I reached the same conclusion, but by a different approach
The 3 digits will be
in hundreds place = cw
in tens place = x(w+c)
in units place = x^2

from stmt 1, all these 3 are equal
hence cw = x(c+w) = x^2 ---- eqn (i)
also, x^2 should be a single digit. so possible values can be 1, 4 and 9.
Hence x can be 1,2 or 3.
But stmt 1 also specifies that the digit in the result is not the same as either of c, w or x. thus x can be 2 or 3 only.
From (i), x = c+w
Thus, c+w-x should be 0.
Thus, answer is (A).

Agree with your explanation for stmt (2).
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w x . X c x ... _____ In the above mutiplication of the two 20 Aug 2006, 01:43
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Professor

from (1) the only three digit number with all same digits is 999 that has factors with same unit digit.
999 = 27 x 37.
so w+c -x = 2+3-7 = -2.

Show more


Proffesor, can you please explain how you obtained 999 ?Did you factorize all the 3 digit numbers having same digits, i.e. 111,222,333,444,555,666,777,888 and 999 ?

I reached the same conclusion, but by a different approach
The 3 digits will be
in hundreds place = cw
in tens place = x(w+c)
in units place = x^2

from stmt 1, all these 3 are equal
hence cw = x(c+w) = x^2 ---- eqn (i)
also, x^2 should be a single digit. so possible values can be 1, 4 and 9.
Hence x can be 1,2 or 3.
But stmt 1 also specifies that the digit in the result is not the same as either of c, w or x. thus x can be 2 or 3 only.
From (i), x = c+w
Thus, c+w-x should be 0.
Thus, answer is (A).

Agree with your explanation for stmt (2).
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prashrash
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w x . X c x ... _____ In the above mutiplication of the two 20 Aug 2006, 01:44
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Professor

from (1) the only three digit number with all same digits is 999 that has factors with same unit digit.
999 = 27 x 37.
so w+c -x = 2+3-7 = -2.

Show more


Proffesor, can you please explain how you obtained 999 ?Did you factorize all the 3 digit numbers having same digits, i.e. 111,222,333,444,555,666,777,888 and 999 ?

I reached the same conclusion, but by a different approach
The 3 digits will be
in hundreds place = cw
in tens place = x(w+c)
in units place = x^2

from stmt 1, all these 3 are equal
hence cw = x(c+w) = x^2 ---- eqn (i)
also, x^2 should be a single digit. so possible values can be 1, 4 and 9.
Hence x can be 1,2 or 3.
But stmt 1 also specifies that the digit in the result is not the same as either of c, w or x. thus x can be 2 or 3 only.
From (i), x = c+w
Thus, c+w-x should be 0.
Thus, answer is (A).

Agree with your explanation for stmt (2).
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w x . X c x ... _____ In the above mutiplication of the two 20 Aug 2006, 06:48
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kevincan
....w x

.X c x
... _____

In the above mutiplication of the two digit 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.
Show more

the clue in st 1 is "The three digits of the product are all the same and different from w c and x". so the three digits are 111, 222, ........999.

if you factorize 111, you get "3 x 37". similarly 222 has "6 x 37", 333 has "9 x 37". therefore all three same digit number have 37 as a factor. so we need another 2 digit factor whose unit digit is 7. so we can easily find such number is 999 because if 111 has 3 and 37, 999 has 27 (9x3) and 37.

actually, when i got the factors (3 and 37) of 111, immidiatly i realized that the three digit number is 999 that has 27 and 37 as the desired values for cx, and wx.

hope it is clear now....
prashrash
Professor

from (1) the only three digit number with all same digits is 999 that has factors with same unit digit.
999 = 27 x 37.
so w+c -x = 2+3-7 = -2.



Proffesor, can you please explain how you obtained 999 ?Did you factorize all the 3 digit numbers having same digits, i.e. 111,222,333,444,555,666,777,888 and 999 ?
Show more



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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