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# GMAT: Data sufficiency 37

142-144, pg. 290. Created by Sal Khan.

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• 143 ) m+x/n+x > m/n
if we cross multiply or simply it further,
n(m+x)> m(n+x)
nm + nx > nm + mx
nm-nm + nx > mx
nx > mx
n > m
i.e m < n ... is it possible to do that way ? that satisfies statement #1 ? • You are very close. The only catch is that the sign flips when you multiply both sides of an inequality by a negative number. In your proof, you multiply both sides twice: once by (n+x) and once by x. If x>0, then (n+x)>0 (since n>0 is given) and so both values are guaranteed to be positive. If x<0, then as long as n<|x|, both x and (n+x) are negative so you still arrive at the conclusion that m<n since the sign flips twice. The only time the inequality doesn't hold is when x is negative but (n+x) is positive, i.e., n>|x|. For example, if x=-1, m=2, and n=3, the inequality becomes (2-1)/(3-1) > 2/3 or 1/2 > 2/3, which is not true. Also, if x=0, then you get m/n > m/n, which is never true.
• For the Question Sal brought up from Problem 142, I think the book was right. The rule of data sufficiency is to judge whether a statement alone is sufficient to lead us to conclude the prompt. If a statement alone is sufficient to disprove the prompt, it is of course "not sufficient to prove the prompt". • i think where you're mistaken is where you say "lead us to conclude the prompt." This is incorrect. It is "verify if the prompt is correct." I.E. 'is x=y?' If you can verify through the clues that the prompt is not correct, you have sufficient evidence to answer the question. For example if the teacher asks you if x=y and you respond 'no', you have answered her question. And thus the clue is sufficient.
• In problem 144, why did Sal multiply both sides of statement 2 by (1/10)? • Q.143: When we give x a negative value just like in the case of -99/-98, the result is positive (negative divided by negative) and still larger than 1/2. Can you please clarify? In this case, I am thinking statement 1 would be enough by itself, what am I missing here?
Thank you so much, great videos, huge help!
(1 vote) • On question 144, I think the alternate method Sal was about to use (min ) would be easier to clarify discussion questions below. ie from the question, one can simplify the question to "is 10^(-n) < 10^(2)?" => is -n<-2? => is n>2?
(1) confirms the simplified question
(2) simplifying the powers gives us 10^(-n+1) < 10^(-1)
=> 1-n<-1 => 2<n (or n>2) - which independently answers the simplified question
(1 vote) • 144)it hasn't been specified in statement 2 that n>2. hence if n were to be 1 and 2, it would contradict the question. so please explain it to me.
(1 vote) • B=x, not 0 