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# This weeks problem from http://www.manhattangmat.com/ I got

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Manager
Joined: 11 Oct 2003
Posts: 102
Location: USA
Followers: 1

Kudos [?]: 0 [0], given: 0

This weeks problem from http://www.manhattangmat.com/ I got [#permalink]  27 Jan 2004, 19:09
This weeks problem from http://www.manhattangmat.com/

I got 40 as the answer. Did anyone else try it?
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Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

it is given that 1)K/L=16 and 2)(K-L)/10=Z then from 1) K=16L and substitute in 2) which gives (16L-L)=10Z or Z=1,5L . We do not know anything about p,q,r,s, ( the powers of L) so think should be E)
Senior Manager
Joined: 05 May 2003
Posts: 427
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

I am also getting 40.

For W to be 16, only b should be greater than q by 4 units. All the others should be equal. Then, Z will be 400/10.
Senior Manager
Joined: 05 May 2003
Posts: 427
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

BG wrote:
it is given that 1)K/L=16 and 2)(K-L)/10=Z then from 1) K=16L and substitute in 2) which gives (16L-L)=10Z or Z=1,5L . We do not know anything about p,q,r,s, ( the powers of L) so think should be E)

K/L is not given as 16.
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

"For numbers K and L, the function W is defined as 5a2b7c3d ├╖ 5p2q7r3s. The function Z is defined as (K тАУ L) ├╖ 10. If W = 16, what is the value of Z?"
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

I solved it as follows
5^a*2^b*7^c*3^d / ( 5^p* 2^q * 7^r * 3^s ) = 16

Only power of 2 is remaining so 2^(b-q) = 16 = 2^4
so b-q = 4, a=p, c=r and d=s
Z = (K-L)/10 = ( 1000(a-p) + 100(b-q) + 10(c-r) + 1(d-s) )/10

= 100 * 4/10 = 40
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