Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
20 Jun 2021, 08:13
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (02:30) correct
74%
(02:45)
wrong
based on 50
sessions
History
Date
Time
Result
Not Attempted Yet
If 0 < a < b < c < d , is \(\frac{ a }{ b } \)< 0.25 ?
1) \(\frac{c + a}{d + b}\) < 0.25
2) \(\frac{c + a}{d + b} < c/d\)
1) \(\frac{c + a}{d + b}\) < 0.25
2) \(\frac{c + a}{d + b} < c/d\)
20 Jun 2021, 14:18
Kudos
Bookmarks
sjuniv32
We know all the variables are positive, so we can translate this question to "is \(a < \frac{1}{4}b\)?"
Statement 1:
d + b must be positive so we can scoot it over to the right side, we get \(a + c < \frac{1}{4}(b + d)\).
We can find \(\frac{1}{4}b - a\) and we can translate the question to "is \(\frac{1}{4}b - a > 0\)?"
Isolate that part on the right side to get \(c - \frac{1}{4}d < \frac{1}{4}b - a \).
We do not know if \(c - \frac{1}{4}d\) if greater than 0, so we cannot tell if \(\frac{1}{4}b - a \) is greater than 0. Insufficient.
Statement 2:
\(cd + ad < cd + cb\)
\(ad < cb\)
\(\frac{a}{b} < \frac{c}{d}\)
We don't know if \(\frac{c}{d}\) is less than 0.25, so insufficient. (If \(\frac{c}{d} < 0.25\) we have \(\frac{a}{b} < \frac{c}{d} < 0.25\) which would be sufficient.)
Combined:
From the 2nd statement we found \(ad < cb\), the left side in statement 1 is \(\frac{c + a}{d + b}\) so let us try to build it starting with a conclusion in statement 2 and see what we can find.
Add ab on both sides: \(ad + ab < cb + ab\)
Factor: \(a(d + b) < b(c + a)\)
Move around the terms: \(\frac{a}{b} < \frac{c + a }{ d + b} < 0.25\)
Conclusion: \(\frac{a}{b} < 0.25\)
Sufficient.
Ans: C
21 Jun 2021, 06:33
Kudos
Bookmarks
sjuniv32
\(\frac{ a }{ b }<\frac{1}{4 }……..b>4a\)?
1) \(\frac{c + a}{d + b}<\frac{1}{4}……….4(c+a)<d+b\)
If d is greater as compared to other variables: a=1, b=2, c=3 and d=20………..4(1+3)<2+20
If a is very small as compared to other variables: a=1, b=5, c=6 and d=30…….4(1+6)<5+30
Insufficient
2) \(\frac{c + a}{d + b} < \frac{c}{d}………..dc+ad<dc +bc……..ad<bc\)
From \( \frac{c + a}{d + b} < \frac{c}{d}\), we can say that \( \frac{a}{b}<\frac{c + a}{d + b} < \frac{c}{d}\). But we cannot compare 1/4 with a/b.
We can easily find lot of cases fitting in both ways.
1*30<6*7 ……..a=1 and b=6
or 1*30<3*11…… a=1 and b=3
Insufficient
Combined
Whenever you have two fractions that are less than 1, the sum of the numerators of both divided by the sum of the denominators is always in between the two fractions in terms of value.
\(\frac{a}{b}<\frac{c + a}{d + b} < \frac{c}{d}\)
\(\frac{a}{b}<\frac{c + a}{d + b} < \frac{1}{4}\)
\(\frac{a}{b}< \frac{1}{4}\)
Sufficient
C
If you want to know some more analysis on fractions
https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html#p2086955
