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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1398
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
If p and q are numbers on the number line above, which of the followin  [#permalink]

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2 00:00

Difficulty:   35% (medium)

Question Stats: 63% (01:02) correct 37% (01:18) wrong based on 169 sessions

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Attachment: 1 (2).jpg [ 19.52 KiB | Viewed 1506 times ]

If p and q are numbers on the number line above, which of the following statements must be true?
I. |p+q | < q
II. p +q < 0
III. pq< 0

A) I only
B) III only
C) I , II
D) I, III
E) II, III

Weekly Quant Quiz #7 Question No 5

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1049
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities)
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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1st statement :

|p+q|<q
-q<p+q<q
Subtracting q
-2q<p<0
From number line q is positive
p is negative.
But p might or might not be less than q. hence this statement is not always true.

2nd statement:

p+q<0
Again depends on p and q.
If q is 30 and p is -10
then p+q is not less than 0
and if p = -5 and q is 3
then -2<0.
Both yes and no.
Not true always.

3rd statement :

P is negative and q is positive.
Hence pq<0.
Always true.

Current Student S
Joined: 04 Jun 2018
Posts: 156
GMAT 1: 610 Q48 V25
GMAT 2: 690 Q50 V32
GMAT 3: 710 Q50 V36
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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If p and q are numbers on the number line above, which of the following statements must be true?
I. |p+q | < q
II. p +q < 0
III. pq< 0

A) I only
B) III only
C) I , II
D) I, III
E) II, III

What we can infer from the image is this:
Both of opposite signs. (p,q) (they are not equal to zero also)
Hence Statement 3 has to be true.

Coming to other statments
Stat 1:
Depends on the distance of p from the 0.
SO if P=-100
and Q=1
Lhs=99
Rhs=1
Which is incorrect
NOt a must be true case

Stat 2:
Again depends on the distance of p from 0 and q from 0

q=5
p=-1
Lhs=4
Hence not a must be true statement

Hence Ans B
Manager  S
Joined: 16 Sep 2011
Posts: 118
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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If p and q are numbers on the number line above, which of the following statements must be true?
I. |p+q | < q
II. p +q < 0
III. pq< 0

----------------------------
p 0 q

which means p<0 and q>0

option A: |p+q| = which is like subtracting some number from q lets say |1-4| <4 true , but consider p as -10 and q as 2 , now |p+q| = 8 which is greater than q so not true always

Option B: p+q<0, now this is also not true lets say -4+3 <0 but how about -1+4 (here p is -1 and q is 4)

Option C: pq<0 always true as p<0 and q>0

Hence B is the answer (III only)
Intern  B
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Posts: 34
Location: India
Schools: IIMA PGPX"20
GPA: 3.5
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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ans is b)only III
as when both of different are multiplied it will be negative
for 1st if it is |-98+1|
the its equal to 97 which is greater than q
and for second any ones magnitude can be greater
Manager  G
Joined: 14 Jun 2018
Posts: 210
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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p is negative ; q is positive

Statement 1 : | -10 + 2 | = 8 ; 8 < 2 = false

Statement 2 : |- 1 + 2 | = 1 ; can be positive = false

Statement 3 : -ve * +ve = -ve = true

B
Manager  S
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Posts: 183
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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1. |P+Q| < Q
Let P = -1 & Q = 1
|-1 + 1| < 1
0<1 [Yes]

Let P = -5 & Q = 10
|-5+10| < 10
5 < 10 [No]

Hence Incorrect

2. P + Q < 0

Let P = -3 & Q = 10
-3 + 10 = 7 [No]

Let P = -1 & Q = 1
-1 + 1 = 0 < 0; they are equal.

Hence incorrect

3. PQ < 0

Let P = -1 & Q = 1
PQ = -1 x 1 = -1
-1 < 0 [Yes]

Let P = -5 & Q = 10
PQ = -5 X 10 = -50
-50 < 0 [Yes]

Hence it is correct

VP  D
Joined: 31 Oct 2013
Posts: 1493
Concentration: Accounting, Finance
GPA: 3.68
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Re: If p and q are numbers on the number line above, which of the followin  [#permalink]

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gmatbusters wrote:
Attachment:
1 (2).jpg

If p and q are numbers on the number line above, which of the following statements must be true?
I. |p+q | < q
II. p +q < 0
III. pq< 0

A) I only
B) III only
C) I , II
D) I, III
E) II, III

Weekly Quant Quiz #7 Question No 5

there is no indication about the value of p and q. we only know that p is negative and q is positive.

so, pq<0. This is the correct answer. Due to range of values of p and q other options are could be true. Re: If p and q are numbers on the number line above, which of the followin   [#permalink] 13 Nov 2018, 11:38
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# If p and q are numbers on the number line above, which of the followin  