Test: Types Of Numbers - GMAT MCQ

Since x is the sum of six consecutive integers, it can be written as:
x = n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)
x = 6n + 15

Note that x must be odd since it is the sum of the even term 6n and the odd term 15, and an even plus an odd gives an odd.

I. TRUE: Since 6n and 15 are both divisible by 3, x is divisible by 3.
II. FALSE: Since x is odd, it CANNOT be divisible by 4. 
III. FALSE: Since x is odd, it CANNOT be divisible by 6. 

The correct answer is A.

If the least number was 3, then 3*4=12<15, does not fulfill the requirement. So, the least number is 4.
If the greatest number is 14, then 14*15=210>200, does not fulfill the requirement.
So, answer is "4 and 13"

1^+5^2+7^2=75, so the sum of there 3 integers is 13.

p²q is a multiple of 5, only can ensure that pq is a multiple of 5. 
So, only (pq)² can surely be a multiple of 25.
 

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

An easy way to add these numbers is as follows:
(29 + 11) + (23 + 7) + (17 + 13) + (2 + 5 + 3) + 19 = 40 + 30 + 30 + 10 + 19 = 129.
The correct answer is D

A------9-----C------8-------D--1--B
A--1--D---8------C------9----------B
Both the two situations can fulfill the requirements.
Answer is E

2-√(5) is less than zero, so √(2-√(5)) is not the real number

xy+z=x(y+z)
xy+z=xy+xz
z=xz
z(x-1)=0
x=1 or z=0
Answer is E