Is p q ? (1) p + r q + s and r s (2) p + s r

Question

Is  p > q  ?

(1)  p + r > q + s  and  r > s 
(2)  p + s < q + r  and  s > r

chetan2u · Answer

Is p > q ? (1) p + r > q + s and r > s say r=-2 and s=-3....... p -2> q -3......p>q-1 ..here p>q when p=4 and q=2 OR p r Add p + s < q + r and s > r .... p + s+r < q + r+s......p

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Condition 2) is equivalent to p > q for the following reason. Since r < s , we have p + r < p + s . Then we have p + r < p + s < q + r or p < r , since p + s < q + r . Thus condition 2) is sufficient. Condition 1) If p = 2, q = 1, r = 2 and s = 1 , then p > q and the answer is 'yes'. If p = 1, q = 2, r = 100 and s = 1 , then p < q and the answer is 'no'. Since condition 1) does not yield a unique solution, it is not sufficient Therefore, B is the answer.

BrentGMATPrepNow · Answer

Target question : Is p > q ? Statement 1 : p + r > q + s and r > s Whenever we're given two inequalities in which the inequality symbols are facing the same direction , we might be able to gain some valuable insights by ADDING the inequalities (see the video below for more on this) So we can take the following inequalities... p + r > q + s r > s .... and ADD for them to get: p + 2r > q + 2s This doesn't help us answer the target question . We can demonstrate this by considering the following values of p, q, r and s that satisfy statement 1: Case a : p = 1, q = 0, r = 5 and s = 1. In this case, the answer to the target question is YES, p is greater than q Case b : p = 0, q = 1, r = 5 and s = 1. In this case, the answer to the target question is NO, p is not greater than q Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : p + s < q + r and s > r Since the two inequality symbols aren't facing the same direction, we can't add the inequalities...YET! One way to get the inequality symbols facing the same direction is to take the second inequality, s > r, and multiply both sides by -1 to get: -s < -r At this point, we can take the following inequalities... p + s < q + r -s < -r ...and ADD them to get: p < q , which means the definitive answer to the target question is NO, p is not greater than q Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B RELATED VIDEO https://www.youtube.com/watch?v=S_fjYmCtvy0

iamcabbage · Answer

Can someone clarify this question in a better way? Also, why are we not using the number substitution method in solving both 1 and 2?

BrentGMATPrepNow · Answer

Number substitution (aka testing values) will only yield definitive results when a statement is not sufficient. More here: https://www.gmatprepnow.com/articles/da ... lug-values

BrentGMATPrepNow · Answer

Target question : Is p > q? Statement 1 : p + r > q + s and r > s Important: We must resist the temptation to subtract the second inequality from the first inequality (to incorrectly conclude that p > q). If we have two inequalities in which the inequality symbols are facing the same direction, we can ADD those inequalities, but we can't subtract them. For more on this, watch the video below. If we take... p + r > q + s r > s ... and ADD them, we get: p + 2r > q + 2s There are several values of p, q, r and s that satisfy the inequality p + 2r > q + 2s . Here are two: Case a : p = 0, q = 1, r = 10 and s = 0. In this case, the answer to the target question is NO, p is not greater than q Case b : p = 1, q = 0, r = 10 and s = 0. In this case, the answer to the target question is YES, p is greater than q Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : p + s < q + r and s > r In this case, we have 2 inequalities, BUT the inequality symbols are not facing the same direction, which means we can't add them...YET! Take the inequality s > r, and multiply both sides by -1 to get: -s < -r We now have the following two inequalities: p + s < q + r -s < -r Now that the inequality symbols are facing the same direction, we can ADD the inequalities to get: p > q . Perfect! Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B RELATED VIDEO https://www.youtube.com/watch?v=S_fjYmCtvy0

Fdambro294 · Answer

Rephrased question: Is: p - q > 0? Statement 1 p - q > s - r And we are also given: r > s Which is the same as: s - r < 0 So the value of (s - r) = some -negative value And statement 1 tells us that: (p - q) > that -negative value So it is possible for: p - q = -negative OR p - q = +positive S1 NOT Sufficient Statement 2: tells us that p - q < r - s …… (inequality I) And we are also given: s > r Or r - s < 0…… (inequality II) Using the Transitive Property of Inequalities for the one stated above in I and II we can therefore say: p - q < r - s < 0 Definite NO: the value of (p-q) must be less than < 0 and can NOT be greater than > 0 p - q < 0 —- s2 sufficient alone *B* Posted from my mobile device

aditijain1507 · Answer

Both options have different relations between r and s, one says that r>s and other says r<s. Experts, is that possible? Isn't the question incorrect?

Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r

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