Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 11:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is q < 0?

Author Message
TAGS:

### Hide Tags

SVP
Joined: 26 Mar 2013
Posts: 2284

### Show Tags

28 Dec 2018, 21:46
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:59) correct 41% (02:15) wrong based on 40 sessions

### HideShow timer Statistics

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: 7764
Re: Is q < 0?  [#permalink]

### Show Tags

28 Dec 2018, 22:04
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
_________________
Manager
Joined: 01 May 2017
Posts: 82
Location: India

### Show Tags

28 Dec 2018, 23:35
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?   [#permalink] 28 Dec 2018, 23:35
Display posts from previous: Sort by