If 3 ＜ x ＜ 100，for how many values of x/3 is the square of a prime number?
A.2
B.3
C.4
D.5
E.9
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Prime Number
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Brent@GMATPrepNow
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Let's begin by listing some prime numbers: 2, 3, 5, 7, 11, 13 . . .GmatKiss wrote:If 3 ＜ x ＜ 100，for how many values of x/3 is the square of a prime number?
A.2
B.3
C.4
D.5
E.9
So, some squares of prime numbers: 2^2, 3^2, 5^2, 7^2, 11^2 . . .
When we evaluate each one, we get 4, 9, 25, 49, 121,...
- For x/3 to equal 4, x must equal 12
- For x/3 to equal 9, x must equal 27
- For x/3 to equal 25, x must equal 75
- For x/3 to equal 49, x must equal a number greater than 100. Since we're told that x<100, we can stop and conclude that there are 3 values of x such that x/3 is the square of a prime number
So, the answer is B
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Brent
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3 ＜ x ＜ 100
1<X/3<100/3
SO, WE HAVE 3 OPTIONS-
3*2^2
3*3^2
3*5^2
1<X/3<100/3
SO, WE HAVE 3 OPTIONS-
3*2^2
3*3^2
3*5^2
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x/3 = square of prime no
multiply by 3 both sides.
x= 3 *( square of prime no i.e 4,9,25,)
product of x and sq of prime no should be less than 100. only 3 products satisfy this condition
3 * 4
3 * 9
3 * 25
3 * 7 > 100
multiply by 3 both sides.
x= 3 *( square of prime no i.e 4,9,25,)
product of x and sq of prime no should be less than 100. only 3 products satisfy this condition
3 * 4
3 * 9
3 * 25
3 * 7 > 100
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Vinoth@GMAT Kolaveri
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