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# Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (

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Intern
Joined: 23 Sep 2015
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Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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29 Sep 2015, 22:05
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65% (hard)

Question Stats:

62% (02:10) correct 38% (02:12) wrong based on 125 sessions

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Is b<50

(1) The square of (b+x) is less than 2500
(2) The square of (b-x) is less than 1500
Jamboree GMAT Instructor
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Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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06 Oct 2015, 00:00
2
S1: (b+x)^2 < 2500

So, b+x < 50 - Not sufficient (w.r.t the value of b)

S2: (b-x)^2<1500

So, (b-x)<39 - Not sufficient (w.r.t the value of b)

After combining : 2b<89, b<48.5 .. Sufficient..
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Aryama Dutta Saikia
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Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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23 Jul 2017, 15:34
2
capsicumgirl wrote:
Is b<50

(1) The square of (b+x) is less than 2500
(2) The square of (b-x) is less than 1500

Here's an approach testing specific cases:

(1) This one simplifies to -50 < b + x < 50.

Case 1: b = 0, x = 0, answer is "yes"
Case 2: b = 100, x = -100, answer is "no"

Not sufficient.

(2) Well, 1500 is a little less than 1600, so the square root should be a little less than 40. If I need to get it more precisely, I can do that later, but for now I'll say '~40' (approximately 40).

~-40 < b - x < ~40

Case 1: b = 0, x = 0, answer is "yes"
Case 2: b = 100, x = -100, answer is "no" (Try to notice chances to reuse cases! That can speed things up.)

Not sufficient.

(1 + 2)
Now I have two inequalities:

~-40 < b - x < ~40
-50 < b + x < 50

Notice that the x and -x will cancel if I add these inequalities together. You can always add any two inequalities whose inequality signs are pointing in the same direction. So, we get this:

~-90 < 2b < ~90
~-45 < b < ~45

We already decided that '~45' is less than 45, since 1500 is less than 1600. So, b is definitely less than 45, and the two statements combined are sufficient.
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Chelsey Cooley | Manhattan Prep | Seattle and Online

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Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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06 Apr 2016, 08:29
Please move to DS. Thank you
capsicumgirl wrote:
Is b<50

(1) The square of (b+x) is less than 2500
(2) The square of (b-x) is less than 1500

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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06 Apr 2016, 08:31
BrushMyQuant wrote:
Please move to DS. Thank you
capsicumgirl wrote:
Is b<50

(1) The square of (b+x) is less than 2500
(2) The square of (b-x) is less than 1500

______________
Done. Thank you.
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Intern
Joined: 25 Mar 2016
Posts: 39
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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23 Jul 2017, 06:17
S1: (b+x)^2 < 2500

So, b+x < 50 - Not sufficient (w.r.t the value of b)

S2: (b-x)^2<1500

So, (b-x)<39 - Not sufficient (w.r.t the value of b)

After combining : 2b<89, b<48.5 .. Sufficient..

at x= 0 we can have largest value for b, which is smaller than 50 and even if we consider negative value for b it will be smaller than 50 so why option A is not sufficient?
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Joined: 05 Mar 2015
Posts: 980
Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (  [#permalink]

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23 Jul 2017, 07:45
PK32 wrote:
S1: (b+x)^2 < 2500

So, b+x < 50 - Not sufficient (w.r.t the value of b)

S2: (b-x)^2<1500

So, (b-x)<39 - Not sufficient (w.r.t the value of b)

After combining : 2b<89, b<48.5 .. Sufficient..

at x= 0 we can have largest value for b, which is smaller than 50 and even if we consider negative value for b it will be smaller than 50 sowhy option A is not sufficient?

Simply because x can be -ve or +ve value....
Re: Is b<50 (1) The square of (b+x) is less than 2500 (2) The square of (   [#permalink] 23 Jul 2017, 07:45
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