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# Z is a two digit positive integer, Z is equal to 7 times the sum of it

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Intern
Joined: 05 Nov 2010
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Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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05 Nov 2010, 09:41
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Difficulty:

65% (hard)

Question Stats:

52% (01:43) correct 48% (01:47) wrong based on 81 sessions

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Z is a two digit positive integer, Z is equal to 7 times the sum of its digits. Is Z = 84?

(1) Sum of its digits is 12
(2) Product of its digits is 32
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Joined: 02 Sep 2009
Posts: 59721
Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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06 Nov 2010, 01:47
2
Creeper300 wrote:
Z is a two digit positive integer, Z is equal to 7 times the sum of its digits. Is Z=84?

1. Sum of its digits is 12
2. Product of its digits is 32

Let the tenths and units digits of Z be $$a$$ and $$b$$ respectively, so $$Z=10a+b$$.

Given: $$Z=10a+b=7(a+b)$$ --> $$a=2b$$ --> $$Z=10a+b=20b+b=21b$$, so Z could take only the following 4 values: 21, 42, 63, and 84.

Question: is $$Z=84$$?

(1) Sum of its digits is 12 --> from the possible values of Z only 84 has the sum of its digits equal to 12. Sufficient.
(2) Product of its digits is 32 --> from the possible values of Z only 84 has the product of its digits equal to 32. Sufficient.

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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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06 Nov 2010, 19:10
good points, the answer should be D. Since 4,8 are the only options. and only 84 is seven times the sum.
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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07 Nov 2010, 00:56
Wow, thank you Bunuel, I would have totally gotten this wrong on the test haha.

Better here than during the real GMAT.
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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07 Nov 2010, 01:39
1
Creeper300 wrote:
Z is a two digit positive integer, Z is equal to 7 times the sum of its digits. Is Z=84?

1. Sum of its digits is 12
2. Product of its digits is 32

let Z = 10a + b, where a is the tens place digit and b is the ones place digit

10a + b = 7 (a+b) => a = 2b ----- (0)

(1) states that the (a+b) = 12
using (1) and (0), the only possible answer is 84

(2) states that axb = 32
using (2) and (0), the only possible answer is 84.
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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09 Nov 2010, 08:55
my brain is not clicking, but can someone explain how a = 2b?

i'm understanding this part: 10a + b = 7 (a+b)
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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09 Nov 2010, 09:05
gtr022001 wrote:
my brain is not clicking, but can someone explain how a = 2b?

i'm understanding this part: 10a + b = 7 (a+b)

Well 10a + b is just another way of writing a two digits number.

For example, if Z = 65, then Z = 65 = 10*6 + 5. where 6 = "a" and 5 = "b"
taking things further, we can express any length number using the notation above.

so if Z = 12345.6 = 10000*1 + 1000*2 + 100*3 + 10*4 + 5 + 0.1*6

and since we are given the fact that Z = 7 * (sum of the digits) = 7* (a+b)
we are able state that 10a + b = 7 (a+b).
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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09 Nov 2010, 09:07
gtr022001 wrote:
my brain is not clicking, but can someone explain how a = 2b?

i'm understanding this part: 10a + b = 7 (a+b)

$$10a + b = 7 (a+b)$$ --> $$10a+b=7a+7b$$ --> $$3a=6b$$ --> $$a=2b$$.

Hope it's clear.
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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10 Nov 2010, 08:33
ah, crystal clear, thanks guys!
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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14 Nov 2010, 23:54
Thanks for post.. Nice question
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it  [#permalink]

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05 Apr 2019, 00:18
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Re: Z is a two digit positive integer, Z is equal to 7 times the sum of it   [#permalink] 05 Apr 2019, 00:18
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