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What is the value of the integer x? (1) x^2 = 81. (2) x is a square

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Bunuel
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What is the value of the integer x? (1) x^2 = 81. (2) x is a square [#permalink] New post   18 Nov 2020, 07:54
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What is the value of the integer x?

(1) x^2 = 81.
(2) x is a square of a prime number.
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C
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Re: What is the value of the integer x? (1) x^2 = 81. (2) x is a square [#permalink] New post   18 Nov 2020, 08:38
Ans : C
1. x^2 = 81
x = +9 or -9
NS
2. x can be any prime no.
On combining, we get x= 9, 9 is square of 3, a prime no
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Re: What is the value of the integer x? (1) x^2 = 81. (2) x is a square [#permalink] New post   18 Nov 2020, 08:40
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We are given that x is an integer. Not necessarily positive though.

(1) we know x is plus or minus 9. Two possibilities means we don’t know the value of x. Not sufficient.

(2) lots of numbers are squares of prime numbers. 4, 9, 25, 49, etc. are all squares of prime numbers. What (2) says is that x is a positive number since it is a square of another integer. Not sufficient.

(1+2) we know that x is plus or minus 9 but x is also positive. This leaves 9 as the only possibility and thus is sufficient. C is correct.

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Re: What is the value of the integer x? (1) x^2 = 81. (2) x is a square [#permalink] New post   18 Nov 2020, 09:39
What is the value of the integer x?

(1) x^2 = 81.
X can be 9 or -9. We get 2 different solutions. Hence Not sufficient.

(2) x is a square of a prime number.
X can be any number that's a square of a prime number. Not sufficient

combining (1) + (2)
From 1 we know that x is either +9 or -9.
From 2, we know that x is a square of a prime number.

The square of prime number cannot be negative, so X=9

option 1 and 2 together are sufficient

Ans: C
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Re: What is the value of the integer x? (1) x^2 = 81. (2) x is a square [#permalink]
18 Nov 2020, 09:39
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Bunuel
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