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(2) (p-1)/q - (p+1)/q <0 p-1-p-1/ q <0 since q is +ve numerator = p-1-p-1 = -2 <0 always true

(3) 1/q < 1/(p+1) ----cancelling p-1 both sides (p+1-q) / q(p+1) <0 as denominator is +ve numerator must be <0 p+1-q <0 p-q < -1-------------(a) if p= 1 , q=2 then NO if p=1 , q=3 then YES Not true

Re: If p and q are positive integers, and p < q, then which of
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26 May 2017, 14:26

2

Top Contributor

1

GMATPrepNow wrote:

If p and q are positive integers, and p < q, then which of the following MUST be true?

I) \(\frac{p}{q} < \frac{p+1}{q+1}\)

II) \(\frac{p–1}{q} < \frac{p+1}{q}\)

III) \(\frac{p–1}{q} < \frac{p–1}{p+1}\)

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

*kudos for all correct solutions

Statement I: There's a nice rule that says "If we add the same positive value to the numerator and denominator of a positive fraction, the resulting fraction is closer to one than the original fraction was. For example (23+8)/(50+8) is closer to 1 than is 23/50

Since p < q, we know that p/q is less than 1 By the above rule, we know that (p+1)/(q+1) is closer to 1 than is p/q, which means p/q < (p+1)/(q+1) < 1 Statement I is TRUE

Statement II: The positive denominators are the same, but the numerator p+1 is greater than p-1 So, it must be the case that (p-1)/q < (p+1)/q Statement II is TRUE

Statement III: This time the numerators are the same, but the denominators are different (q and p+1) We can right away that if p = 1, then the two sides are EQUAL In other words, it is NOT the case that (p–1)/q < (p–1)/(p+1) Statement III need NOT be true

If p and q are positive integers, and p < q, then which of
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11 Jul 2017, 00:53

If we substitute each equation with p=4 and q=8 the outcome is 1. 1/2<5/9=-1<-4 2. 3/8<5/8 = -5<-3 3. 3/8<1/3 = -5<-2 So conclusion should be options 2 & 3.

Please advise why do we get different values on plugging values and directly solving the algebraic expression.

These (-)ve values were assumed as they were considered as integers.

Re: If p and q are positive integers, and p < q, then which of
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11 Jul 2017, 04:25

Top Contributor

FB2017 wrote:

If we substitute each equation with p=4 and q=8 the outcome is 1. 1/2<5/9=-1<-4 2. 3/8<5/8 = -5<-3 3. 3/8<1/3 = -5<-2 So conclusion should be options 2 & 3.

Please advise why do we get different values on plugging values and directly solving the algebraic expression.

These (-)ve values were assumed as they were considered as integers.

I'm confused with the steps you took to make the conclusions in blue above

For example, how does 1/2<5/9 turn into -1<-4?
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Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

If p and q are positive integers, and p < q, then which of
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Updated on: 14 Jul 2017, 00:48

1

GMATPrepNow wrote:

If p and q are positive integers, and p < q, then which of the following MUST be true?

I) \(\frac{p}{q} < \frac{p+1}{q+1}\)

II) \(\frac{p–1}{q} < \frac{p+1}{q}\)

III) \(\frac{p–1}{q} < \frac{p–1}{p+1}\)

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

*kudos for all correct solutions

Given : p<q -> p/q<1

I. p/q . When a constant is added to nr and dr, the fraction tends to move towards 1. Since p/q<1 so (p+1)/(q+1) will move towards 1. Hence p/q < (p+1)/(q+1)

II. (p-1)/q < (p+1)/q.. Since dr. is same and Nr. on right side is greater than left side.

III. (p–1)/q < (p–1)/p+1 .. NOT TRUE . Since p<q -> p+1<=q, So, (p–1)/q <= (p–1)/p+1

Hence only I & II are correct Answer B.
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If p and q are positive integers, and p < q, then which of
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12 Jul 2017, 16:34

shashankism wrote:

GMATPrepNow wrote:

If p and q are positive integers, and p < q, then which of the following MUST be true?

I) \(\frac{p}{q} < \frac{p+1}{q+1}\)

II) \(\frac{p–1}{q} < \frac{p+1}{q}\)

III) \(\frac{p–1}{q} < \frac{p–1}{p+1}\)

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

*kudos for all correct solutions

Given : p<q -> p/q<1

I. p/q . When a constant is added to nr and dr, the fraction tends to move towards 1. Since p/q<1 so (p+1)/(q+1) will move towards 1. Hence p/q < (p+1)/(q+1)

II. (p-1)/q < (p+1)/q.. Since dr. is same and Nr. on right side is greater than left side.

III. (p–1)/q < (p–1)/p+1 .. NOT TRUE . Since p>q -> p+1>q, So, p–1)/q > (p–1)/p+1

Hence only I & II are correct Answer B.

shashankism , I can't follow the bolded part. p isn't greater than q, and in analysis of I you note that, so I think something went wrong here ...?
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Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: If p and q are positive integers, and p < q, then which of
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14 Jul 2017, 00:50

genxer123 wrote:

shashankism wrote:

GMATPrepNow wrote:

If p and q are positive integers, and p < q, then which of the following MUST be true?

I) \(\frac{p}{q} < \frac{p+1}{q+1}\)

II) \(\frac{p–1}{q} < \frac{p+1}{q}\)

III) \(\frac{p–1}{q} < \frac{p–1}{p+1}\)

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

*kudos for all correct solutions

Given : p<q -> p/q<1

I. p/q . When a constant is added to nr and dr, the fraction tends to move towards 1. Since p/q<1 so (p+1)/(q+1) will move towards 1. Hence p/q < (p+1)/(q+1)

II. (p-1)/q < (p+1)/q.. Since dr. is same and Nr. on right side is greater than left side.

III. (p–1)/q < (p–1)/p+1 .. NOT TRUE . Since p>q -> p+1>q, So, (p–1)/q > (p–1)/p+1

Hence only I & II are correct Answer B.

shashankism , I can't follow the bolded part. p isn't greater than q, and in analysis of I you note that, so I think something went wrong here ...?

Yes i didi a mistake over there. I have corrected my solution Basically p < q so p+1<=q and hence (p-1)/q <= (p-1)/(p+1)
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