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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
Updated on: 05 Nov 2023, 11:36
Originally posted by ChandlerBong on 18 Apr 2023, 08:19.
Last edited by ChandlerBong on 05 Nov 2023, 11:36, edited 2 times in total.
Last edited by ChandlerBong on 05 Nov 2023, 11:36, edited 2 times in total.
Kudos
Bookmarks
D
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:
31% (02:01) correct
69%
(01:35)
wrong
based on 42
sessions
History
Date
Time
Result
Not Attempted Yet
If b is a positive number, is \(a^2\) − 2a + b > 0?
(1) a > 2
(2) b > 1
(1) a > 2
(2) b > 1
18 Apr 2023, 12:35
Kudos
Bookmarks
If b is a positive number, is a^2 − 2a + b > 0?
(1) a > 2
(2) b > 1
Given: b>0, since this is Yes No type of data sufficiency question with variable in the question stem, we can plug in values for the variables and check whether statements are giving single answer.
St 1: a>2 Let a = 3 then a^2 = 9, 2a = 2 x 3 = 6 => a^2 − 2a = 9 - 6 = 3 >0
b is also >0, so a^2 − 2a + b > 0--- Yes
In fact, since a>2, a2 - 2a will always be >0.
So, St 1 is sufficient
St 2 : b > 1 but we have no info on a
a can be +ve, -ve or fraction.
If a=0, then a^2 − 2a + b > 0
If a<0, then also a^2 − 2a + b > 0 ( a= -5 then 25+10+b >0)
If a>0, then also a^2 − 2a + b > 0
If a is + fraction say 1/2, then 1/4 - 1 + b = -3/4 + b >0 as b>1, say a= -1/5 then 1/25 - 2/5 + b = -9/25 + b which is again > 0.
So, if b>1, for all values of a
a^2 − 2a + b > 0
St 2 sufficient
Ans : D ( both statements are independently sufficient)
(1) a > 2
(2) b > 1
Given: b>0, since this is Yes No type of data sufficiency question with variable in the question stem, we can plug in values for the variables and check whether statements are giving single answer.
St 1: a>2 Let a = 3 then a^2 = 9, 2a = 2 x 3 = 6 => a^2 − 2a = 9 - 6 = 3 >0
b is also >0, so a^2 − 2a + b > 0--- Yes
In fact, since a>2, a2 - 2a will always be >0.
So, St 1 is sufficient
St 2 : b > 1 but we have no info on a
a can be +ve, -ve or fraction.
If a=0, then a^2 − 2a + b > 0
If a<0, then also a^2 − 2a + b > 0 ( a= -5 then 25+10+b >0)
If a>0, then also a^2 − 2a + b > 0
If a is + fraction say 1/2, then 1/4 - 1 + b = -3/4 + b >0 as b>1, say a= -1/5 then 1/25 - 2/5 + b = -9/25 + b which is again > 0.
So, if b>1, for all values of a
a^2 − 2a + b > 0
St 2 sufficient
Ans : D ( both statements are independently sufficient)
18 Apr 2023, 14:33
Kudos
Bookmarks
ChandlerBong
A couple of observations along the way can help us solve this question without having to test numbers.
Statement 1
(1) a > 2
Two inferences that we can make here -
- a is positive
- \(a^2 - 2a\) is always positive in thi case.
Reasoning: Both \(a^2\) and 2a have 'a' in common. The value of \(a^2\) is obtained by multiplying 'a' with 'a', while the value of 2a is obtained by multiplying 2 with 'a'. While this may seem trivial at first, we are given that a > 2, hence when we multiply 'a' with 'a', we are multiplying a value greater than 2 with 'a', on the other hand, in obtaining '2a' we are multiplying a value equal to 2 with a. Hence \(a^2\) will always be greater than 2a and the difference between \(a^2\) and 2a, i.e. \(a^2 - 2a\) will be always positive.
Thus, \(a^2 − 2a + b\) = positive + b = positive
The statement is sufficient, and we can eliminate B, C, and E.
Statement 2
(2) b > 1
The expression \(a^2 − 2a\) will have its minimum value = -1, when a = 1. Hence if b > 1, the sum of \((a^2 − 2a)\) and b will always be greater than 0.
In other words, \(a^2 − 2a + b > 0\)
This statement is also sufficient to answer the question.
Option D
