HOT Competition 26 Aug/8AM: If p

Question

If  p < 0  and the value of  1 - \frac{p}{q}  is between 0 and 1, then which of the following must be true?

I.  p^2 + q^2 > 1

II.  p + \frac{1}{q} <0

III.  q – p <0

A. Only I
B. Only II
C. Only III
D. I and III
E. II and III

GMATinsight · Answer

Answer: Option E Please check the video for the step-by-step solution. GMATinsight's Solution https://www.youtube.com/watch?v=ot9fJRgFHq4 Screenshot 2020-08-26 at 8.36.02 PM.png

kush09 · Answer

Solution: From question stem, p is -ve and for 1−p/q to be between 0 and 1, q also needs to be -ve (for all +ve value of q, expression will be greater than 1 ) also, q>p, as we need final value +ve, q/p cannot be greater than -1 I. p^2+q^2>1 -- p = -0.03 and q = -0.02, above equation doesn't hold true. II. p+1/q<0 -- as p and q both are negative, this expression will always be true. III. q–p<0 -- as p is smaller than q, this expression will always be negative. So, II and III will be always true. Answer is E.

binsnitin11 · Answer

If p<0 and the value of 1−p/q is between 0 and 1, then which of the following must be true? I. p2+q2>1 II. p+1/q<0 III. q–p<0 A. Only I B. Only II C. Only III D. I and III E. II and III Let try to understand what is given first: 0<1−p/q<1 this imply that 1>p/q>0 also if p and q both positive than q>p and if p and q both negative than q

1 what if p =-0.2 and q = -0.8 option 1 not a must be true 2)p+1/q<0 since both are negative (-ve) +1/(-ve) is always less than 0 so must be true 3)q–p<0 since both are negative and p>q this means that this st. must always be true ex- p=-0.2 and q=-0.4 q-p = -0.4-(-0.2)=-0.2<0 p=-1 q=-3 q-p = -3-(-1) = -2<0 so must be true IMO E (2 & 3)

Tanushka77 · Answer

If p<0 and 0<1-p/q<1 then q must be negative as well. Otherwise they will add up and sum with 1.also, since they are negative p>q. Otherwise the given inequality would not work Statement 1. p^2+q^2>1 this is not necessary the case. Consider p=-0.001 and q=-0,1 Statement 2. They are both negative so it must be true Statement 3. Also True according to the reasoning above. The answer is E Posted from my mobile device

RaghavKhanna · Answer

p < 0
And,
0 < 1 - p/q < 1
-1 < -p/q < 0

Multiply by -1
=> 1 > p/q > 0
=> 0 < p/q < 1

Since, p < 0
=> q < 0 and p > q

III. p > q (proved above)

I. p^2 + q^2 > 1

If, p = -2, q = -1
=> 4 + 1 > 1 ---- True

If, p = -1/3, q = -1/2
=> 1/9 + 1/4 = 13/36 < 1 --- False

=> Reject I.

II. p + 1/q < 0

p - negative
q - negative => 1/q => negative

=> Negative Number + Negative Number = Negative Number < 0 --- True (always)

=> II. And III. Are always true.

Answer: E

Posted from my mobile device

bumpbot · Answer

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HOT Competition 26 Aug/8AM: If p < 0 and the value of 1 - p/q is betwe

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