w x . X c x ... _____ In the above mutiplication of the two

Question

.... 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.

Professor · Answer

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......

kevincan · Answer

Nicely done- I hope it didn't take too long

Professor · Answer

yes!

. 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........

prashrash · Answer

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).

prashrash · Answer

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).

prashrash · Answer

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).

Professor · Answer

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....

w x . X c x ... _____ In the above mutiplication of the two

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