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# M00-05

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:14
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Difficulty:

55% (hard)

Question Stats:

57% (00:55) correct 43% (00:43) wrong based on 98 sessions

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Is $$\frac{75}{z+1}$$ an integer?

(1) $$z = 75x$$ where $$x$$ is an integer

(2) $$0 \le z \le 75$$

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:14
Official Solution:

S1 states that $$z$$ is one of the following: -75, 0, 75, 150, etc. It is not sufficient since when $$z=0$$, the expression is an integer, in all other cases it is not. INSUFFICIENT.

S2 gives a range of numbers where again, the expression may or may not be an integer. INSUFFICIENT.

Combining both statements together, $$z$$ can be 0 or 75. This is again INSUFFICIENT.

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Joined: 16 Apr 2013
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GMAT 1: 760 Q49 V45

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17 Jan 2015, 19:36
From statement 1 alone, can you conclude that the set is evenly spaced?
Math Expert
Joined: 02 Sep 2009
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18 Jan 2015, 02:57
backthatassetup wrote:
From statement 1 alone, can you conclude that the set is evenly spaced?

We don't have a set there... -75, 0, 75, 150, .. are possible values of z.
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18 Jan 2015, 14:09
Bunuel wrote:
backthatassetup wrote:
From statement 1 alone, can you conclude that the set is evenly spaced?

We don't have a set there... -75, 0, 75, 150, .. are possible values of z.

Oops posted my question on the wrong page. Thanks for the response
Intern
Joined: 07 Dec 2014
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17 Mar 2015, 05:10
of z can only take value of 0 or 75, 75/(z+1) will be always integer. Could you please explain if i am missing something?
Math Expert
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17 Mar 2015, 05:30
U81 wrote:
of z can only take value of 0 or 75, 75/(z+1) will be always integer. Could you please explain if i am missing something?

If z = 75, then 75/(z+1) = 75/76, which, as you can see, is not an integer.
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Joined: 07 Dec 2014
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17 Mar 2015, 06:49
Thank you. i missed that.
Current Student
Joined: 21 May 2016
Posts: 16
Location: United Kingdom
GMAT 1: 730 Q49 V41
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30 May 2016, 09:46
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 27 Jan 2011
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17 Jan 2017, 04:19
Combining 1 & 2 we are getting solution 0 and 75. In both these cases the expression 75/z+1 will not be an integer. So why Option C is wrong??
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17 Jan 2017, 05:16
gaurav29 wrote:
Combining 1 & 2 we are getting solution 0 and 75. In both these cases the expression 75/z+1 will not be an integer. So why Option C is wrong??

If z = 0, then 75/(z + 1) = 75/1 = 75 = integer.
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18 Jan 2017, 05:59
1
Is $$\frac{75}{z+1}$$ an integer?

(1) $$z = 75x$$ where $$x$$ is an integer

Test Integer vlaue. ZERO is integer too.

Let x =0 ...........z=0 .........then 75/1 =75...Answer is YES

Let x =1 ...........z=75 .........then 75/76.......Answer is No

Insufficient

(2) $$0 \le z \le 75$$

Test the limits: 0 & 75.. . So the result will as statement 1.

Insufficient

Combining 1 & 2

Same testing values gives same answers.

Intern
Joined: 04 Feb 2014
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14 Jul 2018, 03:05
I've spent almost one hour on this and I don't understand why the solution is not C.

From S(1)
Let x =0 ...........z=0 .........then 75/1 =75...Answer is YES
Let x =1 ...........z=75 .........then 75/76.......Answer is NO
Let x=3.....z=225...then 75/225 not integer answer is NO
And for the rest of x the answer is NO

From S(2), different
Let z=0......then 75/1=75 answer is YES
Let z=2.....then 75/3=25 answer is YES
Let z=4.......then 75/5= 15 answer is YES
Let z=74..... then 75/75=1 answer is YES

From S(1) and S(2) we know that the only value that makes 75/(Z+1) an integer is Z=0. So I consider C correct. Could you please help me see the flaw in my reasoning? Many thanks in advance
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Joined: 26 Mar 2013
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14 Jul 2018, 03:52
1
NatalieStarr wrote:
I've spent almost one hour on this and I don't understand why the solution is not C.

From S(1)
Let x =0 ...........z=0 .........then 75/1 =75...Answer is YES
Let x =1 ...........z=75 .........then 75/76.......Answer is NO
Let x=3.....z=225...then 75/225 not integer answer is NO
And for the rest of x the answer is NO

From S(2), different
Let z=0......then 75/1=75 answer is YES
Let z=2.....then 75/3=25 answer is YES
Let z=4.......then 75/5= 15 answer is YES
Let z=74..... then 75/75=1 answer is YES

From S(1) and S(2) we know that the only value that makes 75/(Z+1) an integer is Z=0. So I consider C correct. Could you please help me see the flaw in my reasoning? Many thanks in advance

Hi NatalieStarr

In statement 2: What if you choose z = 6, will the answer be Yes too? what if z =53, Will the answer still Yes? certainly in both cases the answer is NO. You missed to test other points. You tested only the points that makes the answer yes.

So it is insufficient

Let's combine both statements

From statement 1..........z= 7x

Let's apply this in statement 2

0≤75x≤75..........x could take only 2 integer values 0 & 1.....when z= 0.............answer is yes but when z=75..........Answer is NO

Insufficient too

I hope it helps
Re: M00-05 &nbs [#permalink] 14 Jul 2018, 03:52
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# M00-05

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