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# is the positive integer n equal to the sqaure of an integer

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is the positive integer n equal to the sqaure of an integer [#permalink]  21 Mar 2007, 17:19
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is the positive integer n equal to the sqaure of an integer ?
1. for every prime number p, if p is a divisor of n then so is p^2
2. (n)^1/2 is an integer

what is the value of x ?
1. when x is multiplied by 8, the result is between 50 and 60
2. When x is doubled the result is between 10 and 15.
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Winsome

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is the positive integer n equal to the sqaure of an integer ?
1. for every prime number p, if p is a divisor of n then so is p^2
2. (n)^1/2 is an integer

1. if n = 4 and p = 2, then p^2 = 4 but n could also be 20 and meet that req. INSUFF

2. ((n)^1/2)^2 = n SUFF

So B.

what is the value of x ?
1. when x is multiplied by 8, the result is between 50 and 60
2. When x is doubled the result is between 10 and 15.

1. x can be a decimal number (i.e. 7.1) or an integer 7. INSUFF

2. x can be 6 or 7 (or 7.1). INSUFF

1+2 x can be 7 or 7.1 INSUFF

So E.
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I will go with B and E

For Q1
Stmt 2 is obviously SUFF as its just rephrased stem
Stmt 1 is INSUFF as it mentiones P2 is factor but you can take sample case where P3 is a factor and get inconsistent answer...I mean n can be for example 13*13*13 and therfore wont be suare of an integer.

For Q2
stmt 1 gives 50< 8x < 60 <=> 6.25 < x < 7.5 - INSUFF
stmt 2 gives 10 < 2x < 15 <=> 5 < x < 7.5 - INSUFF

as can be seen x can not be determined even combining 2
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Quote:
what is the value of x ?
1. when x is multiplied by 8, the result is between 50 and 60
2. When x is doubled the result is between 10 and 15.

(E) x can be a mixed number or an integer

Quote:
is the positive integer n equal to the sqaure of an integer ?
1. for every prime number p, if p is a divisor of n then so is p^2
2. (n)^1/2 is an integer

(B)
stmnt. 2 (n)^1/2 = sqrt(n) = (m)(m)=n or (-m)(-m)=n (Sufficient)
stmnt. 1 translates to n >= p*p^2, p may or may not be the only divisors (Insufficient)
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