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22 Apr 2020, 13:38
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A
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Difficulty:
65%
(hard)
Question Stats:
58% (02:11) correct
42%
(02:09)
wrong
based on 296
sessions
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If \(\sqrt{x}\) is a prime number, what is the value of x?
(1) \(-16<-3x+5<22\)
(2) \( x^{2}\) is a two-digit number
(1) \(-16<-3x+5<22\)
(2) \( x^{2}\) is a two-digit number
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
22 Apr 2020, 13:45
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SOLUTION:
Since √x is prime, x>0
(1) \(-16<-3x+5 < 22\)
\(-16-5<-3x+5-5<22-5\)
\(-21<-3x<17\)
\(-7<-x<\frac{17}{3}\)
\(\frac{-17}{3} < x < 7\)
Since x>0 (from the question) the only positive integer that √x = prime is 4.
SUFFICIENT.
(2) x=4 √x= 2, if x=25 √x=5 NOT SUFFICIENT.
ANSWER A
Since √x is prime, x>0
(1) \(-16<-3x+5 < 22\)
\(-16-5<-3x+5-5<22-5\)
\(-21<-3x<17\)
\(-7<-x<\frac{17}{3}\)
\(\frac{-17}{3} < x < 7\)
Since x>0 (from the question) the only positive integer that √x = prime is 4.
SUFFICIENT.
(2) x=4 √x= 2, if x=25 √x=5 NOT SUFFICIENT.
ANSWER A
22 Apr 2020, 13:49
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If \(\sqrt{x}\) is a prime number, what is the value of x?
\(\sqrt{x}=prime\)
\(x=prime^2\)
(1) \(-16<-3x+5<22\);
Subtract 5 from all three parts: \(-21<-3x<17\);
Divide by -3 and flip signs: \(-\frac{17}{3}< x<7\);
x can only be 4 (4 = 2^2 = ptime^2). S
Sufficient.
(2) \(x^{2}\) is a two-digit number.
This implies that x < 10. There are two prime^2 less than 10: 2^2 and 3^2.
Not sufficient.
Answer: A.
\(\sqrt{x}=prime\)
\(x=prime^2\)
(1) \(-16<-3x+5<22\);
Subtract 5 from all three parts: \(-21<-3x<17\);
Divide by -3 and flip signs: \(-\frac{17}{3}< x<7\);
x can only be 4 (4 = 2^2 = ptime^2). S
Sufficient.
(2) \(x^{2}\) is a two-digit number.
This implies that x < 10. There are two prime^2 less than 10: 2^2 and 3^2.
Not sufficient.
Answer: A.
