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Is p>q

by vishalwin » Fri Oct 02, 2015 7:02 am
Is p>q

a) p/q =8/7

b) p^2 > q^2


Can anyone help me?

from b do we get p> +-q ?

also what is answer when p^2 = q^2..........is n't it p = +-q?
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by DavidG@VeritasPrep » Fri Oct 02, 2015 7:57 am
Is p>q

a) p/q =8/7

b) p^2 > q^2


Can anyone help me?

from b do we get p> +-q ?

also what is answer when p^2 = q^2..........is n't it p = +-q?
You could just pick simple numbers here.

For statement 1, say p = 8 and q = 7. p is greater than q, so that's a YES
Say p =-8 and q = -7, p is not greater than q, so that's a NO.

Because we can get a YES or a NO, this statement alone is not sufficient.


Notice that both sets of numbers will also satisfy statement 2. [8^2 > 7^2 and (-8)^2 > (-7)^2]

Because we can use the same sets of numbers, Statement 2 is also not sufficient, and together the statements won't be sufficient, so the answer is E

(If you took the square root of both sides of the inequality in statement 2, you'd end up with |p| > |q|)
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by vishalwin » Fri Oct 02, 2015 8:08 am
Hi Dave,

Thanks for the reply.

I got that from statement B we get magnitude of p is greater than magnitude of q.

I still have a doubt in when we take both stat 1 and stat 2

can't we say p>q or q>p or p> +-q?

Thanks & Regards,
Vishal
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by [email protected] » Fri Oct 02, 2015 9:01 am
Hi Vishal,

You've asked two different questions (one specific and one broad), so let's start with the specific issue about Absolute Values....

The information in Fact 2: P^2 > Q^2 can be translated into |P| > |Q|. This does NOT mean that P is greater than Q though.

If P is negative and Q is positive, then P is NOT greater than Q

eg.

P = -3
Q = 2

Both P^2 > Q^2 and |P| > |Q| are 'satisfied' by these values, but the answer to the given DS question (is P > Q?) would be NO.


As far as the broader DS question (when to 'combine' BOTH Facts), we only do that if we've proven that EACH Fact is insufficient on its own (meaning that the Fact leads to inconsistent answers to the given question). Once we combine the Facts, the goal is the same as it was before - to determine whether the Facts give us enough information to get a consistent answer to the given question.

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by DavidG@VeritasPrep » Sat Oct 03, 2015 9:30 am
I got that from statement B we get magnitude of p is greater than magnitude of q.

I still have a doubt in when we take both stat 1 and stat 2

can't we say p>q or q>p or p> +-q?
Statement 1 tell us that p/q = 8/7, or that p/q = POSITIVE. So we know that p and q are either both positive or both negative. So now, when we evaluate Statement 2, which tells us that |p| > |q| we only have two scenarios to worry about, when the variables are both positive and when the variables are both negative.

If p and q are both positive (say p = 8 and q = 7) then p > q, and clearly p >- q, but the second inequality, while true, isn't terribly helpful in answering the question.

If p and q are both negative (p = -8 and q = -7) then p< q and p < - q, as -q would be positive, but again, the second inequality isn't all that helpful in answering the original question.

The biggest takeaway is that the inequalities we generate will depend on which scenario we're dealing with, so you have to be very careful about generalizing.
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by Max@Math Revolution » Sat Oct 10, 2015 10:46 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is p>q

a) p/q =8/7

b) p^2 > q^2


There are 2 variables (p,q) in the original conditions and we therefore need 2 equations to solve for the variables; the conditions provide 2 equations, so there is high chance that (C) will be the answer.
Looking at the conditions,
the answer to the question is 'yes' for p=8, q=7, but 'no' for p=-8,q=-7. The conditions are insufficient, and (E) is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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