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31 Dec 2022, 04:30
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C
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:
83% (01:06) correct
17%
(01:33)
wrong
based on 83
sessions
History
Date
Time
Result
Not Attempted Yet
If \((3 - √10)x = -1\),what is the value of x?
A. \(3 - √10 \)
B. \(3 - 2√5 \)
C. \(3 + √10 \)
D. \(3 - √5 \)
E. \(3 + √5\)
A. \(3 - √10 \)
B. \(3 - 2√5 \)
C. \(3 + √10 \)
D. \(3 - √5 \)
E. \(3 + √5\)
31 Dec 2022, 07:18
Kudos
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Hi !
Smart question!
First approach(Quick approach-Observe choices and get to the right answer)
\(A^2\) - \(B^2\)= (A+ b)*(A-B)
(3−√10) * (3+√10) = \(3^2\) - \((√10)^2\) = 9-1 = -1. Mark option C.
Second approach-Deep think and get to the right answer.
Don't go to actually solve this question. Deep think and reason this out.
GMAT Track of thought 1
Product of (3−√10) and x is -1 (a negative product).
Since √9 is +3, √10 would be >3 which implies (3−√10) would be negative.
GMAT Track of thought 2
So what do I need to multiply with a negative value (3−√10) to get a negative value which is -1 ?
My answer has to be a positive value.
Knock off A and B.
GMAT Track of thought 3
Observe option D and E. When multiplied with (3−√10), I will be receiving a surd value due to a √5 present in the options. But I need a -1.
Option C has a 3+√10.
If you multiply (3−√10) with (3+√10), you would have \( 3^2\)- \((√10)^2\) = -1
Mark option C.
Hope this is clear
Let me know if you have any questions or concerns.
I look forward to helping you.
Devmitra Sen
GMAT Mentor
Smart question!
First approach(Quick approach-Observe choices and get to the right answer)
\(A^2\) - \(B^2\)= (A+ b)*(A-B)
(3−√10) * (3+√10) = \(3^2\) - \((√10)^2\) = 9-1 = -1. Mark option C.
Second approach-Deep think and get to the right answer.
Don't go to actually solve this question. Deep think and reason this out.
GMAT Track of thought 1Product of (3−√10) and x is -1 (a negative product).
Since √9 is +3, √10 would be >3 which implies (3−√10) would be negative.
GMAT Track of thought 2So what do I need to multiply with a negative value (3−√10) to get a negative value which is -1 ?
My answer has to be a positive value.
Knock off A and B.
GMAT Track of thought 3Observe option D and E. When multiplied with (3−√10), I will be receiving a surd value due to a √5 present in the options. But I need a -1.
Option C has a 3+√10.
If you multiply (3−√10) with (3+√10), you would have \( 3^2\)- \((√10)^2\) = -1
Mark option C.
Hope this is clear
Let me know if you have any questions or concerns.
I look forward to helping you.
Devmitra Sen
GMAT Mentor
