p,q,r,s consecutive no.

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Fri Sep 19, 2014 9:17 am

If p, q, r, and s are consecutive integers, with p<q<r<s, is pr<qs?

(1) pq<rs

(2) ps<qr

Guys ,

Cant we do this question be letting p=1&-1 , q=2&-2 , r=3&-3 , s=4&-4 ?

Pls suggest me..

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 19, 2014 9:17 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Sep 19, 2014 10:47 am

Hi j_shreyans,

This DS question requires that P<Q<R<S AND that the variables be consecutive integers. There are lots of groups of numbers to choose from. We could use:
All positives
P=1
Q=2
R=3
S=4

All negatives
P=-4
Q=-3
R=-2
S=-1

A "mix"
P=-2
Q=-1
R=0
S=1

To address your original question, if P = -1, then the negative values that you chose for the other variables are INCORRECT. P has to be the smallest number (so Q, R and S have to be GREATER than -1)

With that note, you should re-try this question. If you're still unsure of what to do, then post back here and I'll walk you through it.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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pfg2181: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Sep 19, 2014 11:07 am

by pfg2181 » Fri Sep 19, 2014 11:27 am

Rich,

Using your numbers for example:
Statement 1: pq<rs
(1)(2)<(3)(4)--> 2<12 TRUE
(-4)(-3)<(-2)(-1)--> 12<2 FALSE
(-2)(-1)<(0)(1)--> 2<0 FALSE

Statement 1 alone is sufficient.

Statement 2: ps<qr
(1)(4)<(2)(3)--> 4<6 TRUE
(-4)(-1)<(-3)(-2)--> 4<6 TRUE
(-2)(1)<(-1)(0)--> -2<0 TRUE

Statement 2 alone is not sufficient.

Knowing that your integers must be all positives and consecutive, one can reason that pr<qs

ANSWER:
(A)Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question[/u]

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Sep 19, 2014 12:04 pm

Hi pfg2181,

The examples that I offered to j_shreyans were meant to point out a small mistake in her thinking (and to encourage a thorough set of TESTs); they are not a complete set in-and-of themselvesl On certain questions, you would have to do MORE work to be sure that you had gotten the correct answer. That having been said, your answer is correct, but I do want to point out one small mistake in your thinking:

In Fact 1, the 4 values do NOT need to all be positive. You could use the following set of values:

P=-1
Q=0
R=1
S=2

These values "fit" all of the given information (including the info in Fact 1) and would also lead to a YES answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Fri Sep 19, 2014 10:49 pm

Hi Rich ,

I have tested the question will all possible values but didn't come to any conclusion.

for e.g. p=-1 , q=0 , r=1 , s=2

TARGET = pr<qs

statement 1 - pq<rs
(-1)(0)<(1)(2)
0<2 which is true
Now put this value in our target

pr<qs
(-1)(1)<(0)(2)
-1<0 satisfy

Statement 2 - ps<qr
(-1)(2)<(0)(1)
-2<0 - true

Now Target pr<qs

(-1)(1)<(0)(2)
-1<0 also sufficient.

I know i am wrong pls correct me .

I have put lots of time in this question but......uuufffff

OA is A

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Sun Sep 21, 2014 3:23 am

Hi ,

Can you guys pls correct me and let me know where i am wrong?

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Sep 22, 2014 10:12 am

Why not approach it this way:

p = p
q = p + 1
r = p + 2
s = p + 3

We want to know if p * (p + 2) < (p + 1) * (p + 3), which reduces to pÂ² + 2p < pÂ² + 4p + 3, or 0 < 2p + 3, or -3/2 < p. So the real question is "Is p > -3/2?"

S1 gives us p * (p + 1) < (p + 2) * (p + 3), which reduces to pÂ² + p < pÂ² + 5p + 6, or 0 < 4p + 6, or 0 < 2p + 3, or -3/2 < p. Success! SUFFICIENT

S2 gives us p * (p + 3) < (p + 1) * (p + 2), which reduces to pÂ² + 3p < pÂ² + 3p + 2, or 0 < 2. Not very helpful, obviously!

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