[GMAT math practice question]
If 50-√7<x<50+√7, then x=?
1) x is an odd integer
2) √x is an integer.
If 50-√7<x<50+√7, then x=?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: What is the value of x?Max@Math Revolution wrote:[GMAT math practice question]
If 50-√7<x<50+√7, then x=?
1) x is an odd integer
2) √x is an integer.
Given: 50 - √7 < x < 50 + √7
√4 = 2
√9 = 3
So, we can say that √7 = 2.something
This means: 50 - 2.something < x < 50 + 2.something
Simplify to get: 47.something < x < 52.something
Statement 1: x is an odd integer
There are two values of x that satisfy statement 1 (since we also know that 47.something < x < 52.something):
Case a: x = 49
Case b: x = 51
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: √x is an integer
If √x is an integer, then x is a "perfect square"
So, some POSSIBLE values of x are: 1, 4, 9, 16, 25, 36, 49, 64, 81, etc
When we consider the given info (47.something < x < 52.something), we can conclude that x MUST equal 49
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Since 2< √7< 3, we have 47< x < 53 from the original condition '50-√7<x<50+√7'.
Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don't have a unique solution, condition 1) is not sufficient.
Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Since 2< √7< 3, we have 47< x < 53 from the original condition '50-√7<x<50+√7'.
Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don't have a unique solution, condition 1) is not sufficient.
Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.
Therefore, B is the answer.
Answer: B
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]