|
|
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.
26 May 2021, 02:00
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (01:47) correct
15%
(02:21)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
Given that b is more than 90 percent of a, is b < 65?
(1) a > 75
(2) a - b > 5
(1) a > 75
(2) a - b > 5
26 May 2021, 07:04
Kudos
Bookmarks
Bunuel
Target question: Is b < 65?
Given: b is more than 90 percent of a
We can write: b > (9/10)a
Multiply both sides by 10/9 to get: (10/9)b > a
Rearrange: a < (10/9)b
Statement 1: a > 75
Rearrange: 75 < a
Combine with given information to get: 75 < a < (10/9)b
From this, we can conclude: 75 < (10/9)b
Multiply both sides by 9/10 to get: (9/10)75 < b
Simplify: 67.5 < b
If b is greater than 67.5, then we can be certain that b is NOT less than 65.
So, the answer to the target question is NO, b is NOT less than 65
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: a - b > 5
Add b to both sides: a > b + 5
Rearrange: b + 5 < a
Combine with given information to get: b + 5 < a < (10/9)b
From this, we can conclude: b + 5 < (10/9)b
Multiply both sides by 9 to get: 9b + 45 < 10b
Subtract 9b from both sides: 45 < b
So, b could equal 46, in which case b < 65
Conversely, b could equal 100, in which case b > 65
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
29 May 2021, 12:40
Kudos
Bookmarks
Bunuel
Given \(b > 90\%a\), is b < 65?
Statement 1:
Multiply both sides by 90% to get \(90\%*a > 75 - 7.5\) which is \(90\%*a > 67.5\).
Since we have \(b > 90\%*a\) then we can chain the inequalities to find \(b > 90\%*a > 67.5\), therefore \(b > 67.5\) and b cannot be less than 65. Sufficient.
Statement 2:
\(b > 90\%*a\) can be written as \(a < \frac{10}{9}b\). Subtract b on both sides to get \(a - b < \frac{b}{9}\). We also know \(a - b > 5\), thus combining the inequalities give \(5 < \frac{b}{9}\) and \(b > 45\). However we cannot tell if b is less than 65 or not so insufficient.
Ans: A
