the two digit numbers w x and c x

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

the two digit numbers w x and c x

by sanju09 » Sat Aug 14, 2010 3:42 am

In multiplication of the two digit numbers w x and c x, 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, x, and c.
(2) x and w + c are odd numbers.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 14, 2010 3:42 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pm; Thanked: 215 times; Followed by:7 members

by kvcpk » Sat Aug 14, 2010 4:03 am

sanju09 wrote:In multiplication of the two digit numbers w x and c x, 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, x, and c.
(2) x and w + c are odd numbers.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

(1) The three digits of the product are all the same and different from w, x, and c.
(10w+x)(10c+x) =111,222,333,....
111 = 37 *3 .. OUT because none of the digits can be zero.
222 = 37 * 6 .. No common digits.. OUT
333 = 37 * 9.. OUT
444 = 37 * 12. OUT
555 = 37 * 15.. OUT
666 = 37 * 18.. OUT
777 = 37 * 21.. OUT
888 = 37 * 24..OUT
999 = 37 * 27

hence priduct can be 999 only
Hence W=3, X=7, c=2
w+c-x = 8
SUFF

(2) x and w + c are odd numbers.
Let x= 1, w=3, c= 2
31*21 is a 3 digit number
w+c-x = 4
Let x=7, w=1, c=2
17*27 is a 3 digit number
w+c-x = -4
Hence two different answers.
INSUFF

pick A

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