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# Is positive integer z greater than 275?

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Current Student
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Is positive integer z greater than 275? [#permalink]

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12 Sep 2015, 23:23
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Difficulty:

45% (medium)

Question Stats:

64% (00:39) correct 36% (00:50) wrong based on 226 sessions

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Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39

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KUDO me plenty

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Joined: 13 Mar 2013
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WE: Engineering (Telecommunications)
Re: Is positive integer z greater than 275? [#permalink]

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13 Sep 2015, 03:04
1
1
correct ans is E

1) multiple value possible which are both greater and smaller than 275
2) multiple value possible which are both greater and smaller than 275

together 1 and 2

Both no ( 273 ) and yes ( above 275 )

Hence ans E
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Re: Is positive integer z greater than 275? [#permalink]

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16 Sep 2015, 20:04
1
1
Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39

Prime factors of $$275$$ are $$5*5*11$$

Statement 1

Z is a multiple of $$21$$

Prime factors of $$21$$ are $$7*3$$ so if it is only $$7*3$$ the answer will be NO, but if it is $$7*3*5*5*11$$ then the answer will be YES

Insuff

Statement 2

Z is a multiple of $$39$$

Prime factors of $$39$$ are $$13*3$$ so if it is only $$13*3$$ the answer will be NO, but if it is $$13*3*5*5*11$$ then the answer will be YES

Insuff again

Statment 1 and 2

Z is a multiple of $$21$$ and $$39$$ (LCM of Z is $$3*7*13$$)

So, if Z is $$3*7*13$$ the answer will be NO, but if Z is $$3*7*13*2$$ the answer will be YES

Insuff

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Re: Is positive integer z greater than 275? [#permalink]

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27 Sep 2017, 00:53
Is positive integer z greater than 275?

(1) z is a multiple of 21
z is multiple of 21 => z can be = 21,42.....
Clearly Insufficient

(2) z is a multiple of 39
z is multiple of 39 => z can be = 39,78.....
Clearly Insufficient

1+2
Z is multiple of 21 and 39 => minimum value of z = LCM of 21 and 39 = 3*7*13 = 273
So here we have atleast 1 value of z less than 275
Insufficient

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Re: Is positive integer z greater than 275? [#permalink]

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27 Sep 2017, 04:32
Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39

Statement 1
The value of the multiple can be greater than 275 of lesser than 275 hence insufficient
Statement 2
Again the value can greater or lesser than 275 not sufficient
Taking both the statements together
We have LCM of 21 and 39 =273
Thus it can also be greater than or lesser than 275
So insufficient

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Re: Is positive integer z greater than 275? [#permalink]

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28 Apr 2018, 06:44
Top Contributor
Is positive integer z greater than 275?

(1) z is a multiple of 21
(2) z is a multiple of 39

Target question: Is positive integer z greater than 275?

Statement 1: z is a multiple of 21
Let's TEST some values.
There are several values of z that satisfy statement 1. Here are two:
Case a: z = 21, in which case, the answer to the target question is NO, z is NOT greater than 275
Case b: z = 2100, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z is a multiple of 39
Let's TEST values again.
Case a: z = 39, in which case, the answer to the target question is NO, z is NOT greater than 275
Case b: z = 3900, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that z is a multiple of 21, which means we can write z = 21k for some integer k
Statement 2 tells us that z is a multiple of 39, which means we can write z = 39j for some integer j
Saying that z = 21k is the same as saying that z = (3)(7)(k)
Saying that z = 39j is the same as saying that z = (3)(13)(j)
When we write z is these two ways, we can see that (3)(7)(13) will be a multiple of 21 AND a multiple of 39
(3)(7)(13) = 273, so z COULD equal 273, in which case, the answer to the target question is NO, z is NOT greater than 275
Or it could be the case that z = (3)(7)(13)(2) = 546, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Is positive integer z greater than 275?   [#permalink] 28 Apr 2018, 06:44
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