When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x  y?
If n is a positive integer, what is the remainder when 3^{8n+3} + 2 is divided by 5?
What is the remainder when the positive integer n is divided by the positive integer k, where k > 1?
1) n = (k+1)^{3}
2) k = 5
What is the remainder when the sum of the positive integers x and y is divided by 6?
1) When x is divided by 6, the remainder is 3. ?
2) When y is divided by 6, the remainder is 1.
When 20 is divided by the positive integer k, the remainder is k – 2. Which of the following is a possible value of k?
Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?
1) The range of the seven remainders is 6. ?
2) The seven numbers selected are consecutive integers. ?
Correct Answer : b
Explanation : The trick here is to know that remainder is always nonnegative integer less than divisor 0≤r<d0≤r<d, so in our case 0≤r<70≤r<7.
So the remainder upon division of any integer by 7 can be: 0, 1, 2, 3, 4, 5, or 6 (7 values).
(1) The range of the seven remainders is 6 > if we pick 6 different multiples of 7 (all remainders 0) and the 7th number 6 (remainder 6) then the range would be 6 and the sum also 6. But if we pick 7 consecutive integers then we'll have all possible remainders: 0, 1, 2, 3, 4, 5, and 6 and their sum will be 21. Not sufficient.
(2) The seven numbers selected are consecutive integers > ANY 7 consecutive integers will give us all remainders possible: 0, 1, 2, 3, 4, 5, and 6. It does not matter what the starting integer will be: if it's say 11 then the remainder of 7 consecutive integers from 11 divided by 7 will be: 4, 5, 6, 0, 1, 2, and 3 and if starting number is say 14 then the remainder of 7 consecutive integers from 14 divided by 7 will be: 0, 1, 2, 3, 4, 5 and 6. So in any case sum=0+1+2+3+4+5+6=21. Sufficient.
When 15n, where n is a positive integer, is divided by 6, the remainder is x. What is the value of x?
1) When n is divided by 2, the remainder is 0. ?
2) When n is divided by 3, the remainder is 0. ?
If n is a positive integer, what is the remainder when (7^{(4n+3)})(6^{n}) is divided by 10?
For a nonnegative integer n, if the remainder is 1 when 2^{n} is divided by 3, then which of the following must be true?
I. n is greater than zero. ?
II. 3^{n} = (3)^{n} ?
III. (√2)^{n} is an integer.
If n is a positive integer and r is the remainder when (n – 1)(n + 1) is divided by 24, what is the value of r?
1) 2 is not a factor of n. ?
2) 3 is not a factor of n.
What is the remainder when the twodigit, positive integer x is divided by 3 ?
1) The sum of the digits of x is 5.?
2) The remainder when x is divided by 9 is 5.
What is the remainder when the positive integer x is divided by 8?
1) When x is divided by 12, the remainder is 5. ?
2) When x is divided by 18, the remainder is 11. ?
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?
The remainder is 9 when x is divided by y, so x = yq + 9 for some positive integer q.
Dividing both side by y give x/y = q + 9/y
But x/y = 96.12 = 96 + 0.12
Equating the two expressions for x/y give q + 9/y = 96 + 0.12
Thus q = 96 and 9/y = 0.12
⇒ 9 = 0.12y
⇒ y = 9/0.12
⇒ y = 75
For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of ( (98 Θ 33) Θ 17 )− ( 98 Θ (33 Θ 17) ) ?
First for ((98 Θ 33) Θ 17), determine 98 Θ 33, which equalsd to 32, since 32 is remainder when 98 divided with 33 ( 98 = 2(33) + 32 ).
Then determine 32 Θ 17 which equals to 15, since 15 is the remainder when 32 is divided by 17( 33= 1(17) +15)
Thus ( (98 Θ 33) Θ 17 ) = 15
Next, for (98 Θ (33 Θ 17)) , determine 33 Θ 17, which equalsd to 16, since16is remainder when33 divided with17 ( 33 = 1(17) + 16 ).
Then determine 98 Θ 16 which equals to 2, since 2 is the remainder when 98 is divided by 16 ( 98 = 6(16) + 2)
Thus (98 Θ (33 Θ 17)) = 2
Finally ((98 Θ 33) Θ 17)− (98 Θ (33 Θ 17)) = 15  2 = 13
How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49
A total of 17 numbers are there which gives a remainder 1 when divided by 3
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 








