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30 Mar 2020, 16:50
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A
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Difficulty:
25%
(medium)
Question Stats:
78% (01:31) correct
22%
(01:24)
wrong
based on 51
sessions
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Date
Time
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If a and b are non-negative integers, is √a + √b = 1 ?
(1) √a + √b = 2√a + 2√b
(2) √a < 3
(1) √a + √b = 2√a + 2√b
(2) √a < 3
Attachment:
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Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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30 Mar 2020, 17:49
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ST (1) : √a+√b=2√a+2√b
=> 2(√a+√b)-(√a+√b) = 0
=> √a+√b = 0
so , √a+√b ≠ 1 , sufficient
ST (2) : √a<3
=> √a<1.732..
so, a = 0 or 1
we don't know about b .
if b = 0 , a= 0 : √a+√b =0
but , if b=0 , a=1 : √a+√b =1
so, ST (2) is not sufficient
correct answer is A
=> 2(√a+√b)-(√a+√b) = 0
=> √a+√b = 0
so , √a+√b ≠ 1 , sufficient
ST (2) : √a<3
=> √a<1.732..
so, a = 0 or 1
we don't know about b .
if b = 0 , a= 0 : √a+√b =0
but , if b=0 , a=1 : √a+√b =1
so, ST (2) is not sufficient
correct answer is A
31 Mar 2020, 19:00
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TheNightKing
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.
Visit https://www.mathrevolution.com/gmat/lesson for details.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Condition 1)
√a + √b = 2√a + 2√b
⇔ √a + √b = 0
⇔ a = b = 0.
The answer is 'no'.
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.
Condition 2)
If a = 1 and b = 0, then we have √a + √b = 1 and the answer is 'yes'.
If a = 1 and b = 1, then we have √a + √b = 2 and the answer is 'no'.
Since condition 2) does not yield a unique solution, it is not sufficient.
Therefore, A is the answer.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
