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# Is the range of the integers 4, 7, x, 6, 5, y greater than 9

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Is the range of the integers 4, 7, x, 6, 5, y greater than 9 [#permalink]

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01 Sep 2013, 05:25
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Is the range of the integers 4, 7, x, 6, 5, y greater than 9 ?

(1)$$y > x^2$$
(2) 3 < x < y

Can someone explain, not satisfied with the explanation provided by TOTAL GMAT MATH, jeff sackmann!

Thanks
[Reveal] Spoiler: OA
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Re: Is the range of the integers 4, 7, x, 6, 5, y greater than 9 [#permalink]

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01 Sep 2013, 05:55
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akhilright wrote:
Is the range of the integers 4, 7, x, 6, 5, y greater than 9 ?

(1) $$y > x^2$$
(2) 3 < x < y

Can someone explain, not satisfied with the explanation provided by TOTAL GMAT MATH, jeff sackmann!

Thanks

From F.S 1, for x=0,y=1, we have the range as : 7-0 = 7<9. Thus, a NO. Again, for x=4,y=17, we have the range as 17-4 = 13>9. Thus a YES. Insufficient.

From F.S 2, the minimum value of x=4. Thus, just as above, for x=4,y=17, the range is 13,a YES. And, for x=4,y=5, the range is 7-4 = 3<9. Thus a NO. Insufficient.

Taking both together, we know that x is atleast 4, and thus, y>16. Thus, y is atleast 17, and the range is atleast = 17-4 = 13(Which is greater than 9). Sufficient.

C.

BTW, an inspired question from the OG.
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Re: Is the range of the integers 4, 7, x, 6, 5, y greater than 9 [#permalink]

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01 Sep 2013, 05:57
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Expert's post
Is the range of the integers 4, 7, x, 6, 5, y greater than 9 ?

The range of a set is the difference between the largest and smallest elements of the set.

(1) y > x^2. Clearly insufficient. If y=4 and x=0, then the range is 7-0=7<9 but if y=100 and y=0, the the range is 100-0=100>9. Not sufficient.

(2) 3 < x < y. Also insufficient. Consider (x, y)=(4, 5) and (x, y)=(4, 100).

(1)+(2) Since x is an integer greater than 3, then the leas value of x is 4 (and the least value of x^2 is 16). From (1) we have that y > x^2, so the least value of y is 17, which mean that the least value of the range is 17-4=13>9. Sufficient.

Hope it's clear.
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Re: Is the range of the integers 4, 7, x, 6, 5, y greater than 9 [#permalink]

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01 Sep 2013, 20:30
Thank you mau5 and Bunuel !
Re: Is the range of the integers 4, 7, x, 6, 5, y greater than 9   [#permalink] 01 Sep 2013, 20:30
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