prime factor of 899 is x

sanju09 wrote:The smallest prime factor of 899 is x. Which of the following is true of x?
a. 1 < x ≤ 7
b. 7 < x ≤ 14
c. 14 < x ≤ 21
d. 21 < x ≤ 28
e. 28 < x ≤ 35

[spoiler]Source: Manhattan GMAT Challenge Problem of the Week – 25 May 2010[/spoiler]

899 = 29 *31

Pick E

gmatmachoman wrote:

sanju09 wrote:The smallest prime factor of 899 is x. Which of the following is true of x?
a. 1 < x ≤ 7
b. 7 < x ≤ 14
c. 14 < x ≤ 21
d. 21 < x ≤ 28
e. 28 < x ≤ 35

[spoiler]Source: Manhattan GMAT Challenge Problem of the Week – 25 May 2010[/spoiler]

899 = 29 *31

Pick E

Hi Govind,

How quickly can one identify that 899 is not divisible by a prime less than 29? Would you suggest "trial and error" way or what went through your mind?

I generally find the square root of the number and find the closest prime number and look in to the options

In our case : X = 899

VX (sqrt X)is equivalent to 30. Look for prime numbers near to 30...Say 29 ,31 is there. SO do the math from there on


Another example : X = 400

VX = 20

5*(2 ^2)*5*(2^2). Pick 2 as smallest prime number.

gmatmachoman wrote:

sanju09 wrote:The smallest prime factor of 899 is x. Which of the following is true of x?
a. 1 < x ≤ 7
b. 7 < x ≤ 14
c. 14 < x ≤ 21
d. 21 < x ≤ 28
e. 28 < x ≤ 35

[spoiler]Source: Manhattan GMAT Challenge Problem of the Week – 25 May 2010[/spoiler]

899 = 29 *31

Pick E

It's good to realize that 900 is a perfect square, and thus 899 = 30^2 - 1^2 = 31 * 29

kevincanspain wrote:

gmatmachoman wrote:

sanju09 wrote:The smallest prime factor of 899 is x. Which of the following is true of x?
a. 1 < x ≤ 7
b. 7 < x ≤ 14
c. 14 < x ≤ 21
d. 21 < x ≤ 28
e. 28 < x ≤ 35

[spoiler]Source: Manhattan GMAT Challenge Problem of the Week – 25 May 2010[/spoiler]

899 = 29 *31

Pick E

It's good to realize that 900 is a perfect square, and thus 899 = 30^2 - 1^2 = 31 * 29

That's brilliant only after realizing a nearby perfect square that could work like that, thanks Govind and kevincanspain for such useful inputs.