If 4

Question

If 4 < x < 100, for how many values of x is  \frac{x}{4}  square of an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

Bunuel · Answer

4 < x < 100 ;

1<\frac{x}{4}<25  (just divide all parts of the inequality by 4).

\frac{x}{4}  should be the square of an integer, thus  \frac{x}{4}  could be 2^2 = 4, 3^2 = 9 or 4^2 = 16 (x could be 16, 36, or 64, respectively).

Answer: B.

Bunuel · Answer

Similar question from OG: https://gmatclub.com/forum/if-3-x-100-f ... 44069.html

sashiim20 · Answer

4 < x < 100

Squares between  4  and  100  are  = 9, 16, 25, 36, 49, 64, 81

Out of the above numbers, numbers that are divisible by  4 = 16, 36, 64

Therefore  x  could be  = 16, 36, 64

Checking  \frac{x}{4}  is square;

\frac{16}{4} = 4 ------ (2^2)

\frac{36}{4} = 9 ------ (3^2)

\frac{64}{4} = 16 ------ (4^2)

Hence total number of values of  x  where  \frac{x}{4}  is square of an integer  = 3

Answer (B)...

diksharautt · Answer

4<x<100

= I^2

Therefore, x = 4*I^2

If I = 1

x = 4 (but x>4)

Therefore, I = 2

x = 16

Similarly, x = 36, 64

when I = 5

x = 100 (However, x is less than 100)

Therefore, the only values are 3. x = 16, 36, 64 (I = 2,3,4)

onlymalapink · Answer

is it weird that the wording of the question just didnt make sense to me?

A_Nishith · Answer

4<x<100;

1<(x/4)<25 (just divide all parts of the inequality by 4).

x/4 should be the square of an integer, 
thus x/4 could be 2^2 = 4, 3^2 = 9 or 4^2 = 16 (x could be 16, 36, or 64, respectively).

Answer: B

If 4 < x < 100, for how many values of x is x/4 square of an integer?

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