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# Is q < 0?

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SVP
Joined: 26 Mar 2013
Posts: 2005

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28 Dec 2018, 20:46
00:00

Difficulty:

65% (hard)

Question Stats:

63% (01:32) correct 38% (02:07) wrong based on 24 sessions

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Is q < 0?

1) on the number line, (q - 15) is closer to 0 than q is

2) on the number line, (q - 15) is closer to 0 than to q

Source: Expert Global
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: Is q < 0?  [#permalink]

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28 Dec 2018, 21:04
1
Is q < 0?

1) on the number line, (q - 15) is closer to 0 than q is
If q is negative, then (q-15) will become even smaller and further from 0 than q is, so q has to be positive
OR this tells us that |q|>|q-15|...
Square both sides as both are positive..
$$q^2>q^2-30q+225.....30q>225....q>7.5$$..
Thus answer is always NO, q is not less than 0
Sufficient

2) on the number line, (q - 15) is closer to 0 than to q
So q is farther from 0 as compared to q-15..
This is exactly what statement I tells you..
Same solution as for statement I
Sufficient

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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28 Dec 2018, 22:35
1) if q is negative q-15 should be more far from 0 than q, because if a negative number is added to another negative number it Magnitude increases but on the negative side.
But given q-15 is closer to 0 than q, which implies q >= 0

So, q not less than 0 (Sufficient)

2) on the number line, (q - 15) is closer to 0 than to q => |q-15| < |q| (distance on a number line)

case(i) consider q> 0
q=1
q-15 = -14
Contradiction q-15 not close to 0 than q
=> q>7
So, Clearly it's a No (sufficient)

case(ii) q<0 or q<7
q = -1
q-15 = -16

Clear we can see, q >7 which is Sufficient

Both A and B are individually sufficient

So, Option D is correct
Is q < 0? &nbs [#permalink] 28 Dec 2018, 22:35
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