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Z is a two digit positive integer, Z is equal to 7 times the [#permalink]
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05 Nov 2010, 09:41
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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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Re: Z is a two digit [#permalink]
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05 Nov 2010, 10:15
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 Original Statement: Z = a b , expressing tens digit as a and ones digit as b. Z = 7(a+b) is Z = 84? Statement 1: a + b = 12 > Z = 7 (12) = 84 Sufficient. Statement 2: a * b = 32 Factors of 32: 2*16 and 4*8 since a and b has to be single digit 4 and 8 are the only possible choice for a and b. so Z can be 48 or 84. Not sufficient My answer is A.



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Re: Z is a two digit [#permalink]
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05 Nov 2010, 22:16
no OA, i believe A can also be 48, 84



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Re: Z is a two digit [#permalink]
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05 Nov 2010, 22:22
Well original statement says that z = 7 * sum of the digits.
Statement 1 says sum of the digits is 12. so z = 7 * 12 = 84.
is order for z to be 48 it the sum of the digits would have to be 48/7 which is not equal to 12.



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Re: Z is a two digit [#permalink]
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06 Nov 2010, 01:21
According to the question, Z= 7 (x+y), where x and y are the digits of Z
Statement 1: x+y = 12
Hence substitute this in z= 7 (x+y) Therefore, Z = 7[*]12 = 84
Statement 1 is sufficient.
Statement 2: xy= 32
we get the following combination for (x,y): 32,1 2, 16 8,4
Thus Statement 2 is in sufficient
So OA is A



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Re: Z is a two digit [#permalink]
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06 Nov 2010, 01:47
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. Answer: D.
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Re: Z is a two digit [#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 [#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 [#permalink]
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07 Nov 2010, 01:39
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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 [#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 [#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 [#permalink]
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09 Nov 2010, 09:07



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Re: Z is a two digit [#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 [#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 [#permalink]
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05 Jan 2011, 15:25
The answer is D. The number has to be divided 7. So there is only option; 84 Posted from GMAT ToolKit



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Re: Z is a two digit positive integer, Z is equal to 7 times the [#permalink]
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19 Feb 2017, 12:27
chaoswithin wrote: 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 Original Statement: Z = a b , expressing tens digit as a and ones digit as b. Z = 7(a+b) is Z = 84? Statement 1: a + b = 12 > Z = 7 (12) = 84 Sufficient. Statement 2: a * b = 32 Factors of 32: 2*16 and 4*8 since a and b has to be single digit 4 and 8 are the only possible choice for a and b. so Z can be 48 or 84. Not sufficient My answer is A. In the stem it is already given that Z is 7 times sum of its digit. Posted from my mobile device



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Re: Z is a two digit positive integer, Z is equal to 7 times the [#permalink]
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24 Feb 2017, 04:47
ramgmat wrote: According to the question, Z= 7 (x+y), where x and y are the digits of Z
Statement 1: x+y = 12
Hence substitute this in z= 7 (x+y) Therefore, Z = 7[*]12 = 84
Statement 1 is sufficient.
Statement 2: xy= 32
we get the following combination for (x,y): 32,1 2, 16 8,4
Thus Statement 2 is in sufficient
So OA is A Hi, z is a 2 digit number, so the 32,1 pair is not an option




Re: Z is a two digit positive integer, Z is equal to 7 times the
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