If x is the sum of six consecutive integers, then x is divisible by which of the following:
I. 3
II. 4
III. 6
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.
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
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"
The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
1^+5^2+7^2=75, so the sum of there 3 integers is 13.
If n is a multiple of 5 and n= p^{2}q, where p and q are prime numbers, which of the following must be a
multiple of 25?
p^{2}q 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.
What is the sum of the first 10 prime numbers?
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
For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b?
A9C8D1B
A1D8C9B
Both the two situations can fulfill the requirements.
Answer is E
For which of the following values of x is {1[2(x^{1/2})]^{1/2}}^{1/2} not defined as a real number?
2√(5) is less than zero, so √(2√(5)) is not the real number
If xy +z =x(y+z), which of the following must be true?
xy+z=x(y+z)
xy+z=xy+xz
z=xz
z(x1)=0
x=1 or z=0
Answer is E
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