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K and L are each four-digit positive integers with thousands [#permalink]
15 Nov 2009, 11:58

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Difficulty:

35% (medium)

Question Stats:

70% (02:59) correct
29% (02:29) wrong based on 85 sessions

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Re: Number Properties [#permalink]
15 Nov 2009, 12:24

3

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Expert's post

ctrlaltdel wrote:

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Re: Number Properties [#permalink]
15 Nov 2009, 16:54

Expert's post

flgators519 wrote:

where did the 400 come from? Thanks

We got that in two 4 digit numbers abcd and pqrs all numbers except b and q are the same and b-q=4. abcd=1000a+100b+10c+d and pqrs=1000p+100q+10r+s. abcd-pqrs=1000a+100b+10c+d-(1000p+100q+10r+s) as a=p, c=r and d=s, we'll get 100b-100q=(b-q)*100=4*100=400.

Re: Number Properties [#permalink]
15 Nov 2009, 16:57

1

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Bunuel wrote:

ctrlaltdel wrote:

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Re: Functions - concepts testing [#permalink]
03 Mar 2010, 03:35

1

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D

Again, I think my way is kinda slow but here goes:

K = 1000a + 100b + 10c + d L = 1000p + 100q + 10r + s

W = (5^a 2^b 7^c 3^d)/(5^p 2^q 7^r 3^s) = 16 W = 5^(a-p) 2^(b-q) 7^(c-r) 3(d-s) = 16

Next you do a prime factorisation of 16 and get 2^4 Thus, we know that 2 is the only prime factor of 16, and since the other numbers in W are also prime, we can deduce the following: a-p = 0 b-q = 4 c-r = 0 d-s = 0

Keeping the statements above in mind, when we evaluate K-L we get: (100b-100q)/10 = Z (100(b-q))/10 = Z (100*4)/10 = Z = 40

Re: K and L are each four-digit positive integers with thousands [#permalink]
09 Nov 2013, 18:53

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Re: K and L are each four-digit positive integers with thousands [#permalink]
30 Dec 2013, 12:41

ctrlaltdel wrote:

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.