|
|
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.
22 Oct 2019, 20:01
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:02) correct
36%
(02:02)
wrong
based on 99
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \(|\frac{a}{b}|\)?
(1) \(\frac{a+b}{a}=1\frac{3}{4}\)
(2) \(\frac{a+b}{a-b}+\frac{a-b}{a+b}=7\frac{1}{7}\)
(1) \(\frac{a+b}{a}=1\frac{3}{4}\)
(2) \(\frac{a+b}{a-b}+\frac{a-b}{a+b}=7\frac{1}{7}\)
Chetan's tricky questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
23 Oct 2019, 12:36
Kudos
Bookmarks
From Statement 1,
1 + (b/a) = 1 + (3/4)
b/a = 3/4
so |a/b| = 4/3, and Statement 1 is sufficient.
For Statement 2, the two terms in the sum on the left side are reciprocals of each other. If we let x = (a+b)/(a-b), the equation becomes
x + (1/x) = 7 + (1/7)
and we can immediately see that x = 7 and x = 1/7 are two solutions to this equation. Since we'd get a quadratic if we multiply both sides by x, the equation can have at most two solutions, so those are the only two solutions for x. So either
7 = (a + b)/(a - b)
7a - 7b = a + b
6a = 8b
|a/b| = 8/6 = 4/3
or
1/7 = (a + b)/(a-b)
a-b = 7a + 7b
-6a = 8b
|a/b| = |8/(-6)| = 4/3
and since in each case we get the same value for |a/b|, Statement 2 is sufficient and the answer is D.
1 + (b/a) = 1 + (3/4)
b/a = 3/4
so |a/b| = 4/3, and Statement 1 is sufficient.
For Statement 2, the two terms in the sum on the left side are reciprocals of each other. If we let x = (a+b)/(a-b), the equation becomes
x + (1/x) = 7 + (1/7)
and we can immediately see that x = 7 and x = 1/7 are two solutions to this equation. Since we'd get a quadratic if we multiply both sides by x, the equation can have at most two solutions, so those are the only two solutions for x. So either
7 = (a + b)/(a - b)
7a - 7b = a + b
6a = 8b
|a/b| = 8/6 = 4/3
or
1/7 = (a + b)/(a-b)
a-b = 7a + 7b
-6a = 8b
|a/b| = |8/(-6)| = 4/3
and since in each case we get the same value for |a/b|, Statement 2 is sufficient and the answer is D.
25 Oct 2019, 20:07
Kudos
Bookmarks
chetan2u
IanStewart, great solution..
Another way would be...
(1) \(\frac{a+b}{a}=1\frac{3}{4}\)...
\(1+\frac{b}{a}=1+\frac{3}{4}.......\frac{b}{a}=\frac{3}{4}.........\frac{a}{b}=\frac{4}{3}\)...
(2) \(\frac{a+b}{a-b}+\frac{a-b}{a+b}=7\frac{1}{7}\)
Divide by b.....\(\frac{\frac{a}{b}+\frac{b}{b}}{\frac{a}{b}-\frac{b}{b}}+\frac{\frac{a}{b}-\frac{b}{b}}{\frac{a}{b}+\frac{b}{b}}=7\frac{1}{7}\)........\(\frac{\frac{a}{b}+1}{\frac{a}{b}-1}+\frac{\frac{a}{b}-1}{\frac{a}{b}+1}=7\frac{1}{7}\)
Let \(\frac{a}{b}=x\)..
\(\frac{x+1}{x-1}+\frac{x-1}{x+1}=7\frac{1}{7}..........\frac{(x^2+2x+1)+(x^2-2x+1)}{x^2-1}=\frac{50}{7}.....\frac{2x^2+2}{x^2-1}=\frac{50}{7}........14x^2+14=50x^2-50.....36x^2=64....x^2=\frac{64}{36}.....|x|=\frac{8}{6}=\frac{4}{3}\)
D
