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Question 1 of 5
1. Question
If x and y are positive integers such that (3x + 7y ) is a multiple of 11, then which of the following will also be divided by 11?
Correct
Ans : D
Keeping y =1, for x = 5, we have 3x + 7y =22 which is divisible by 11.
Now, substitute x =5 and y =1 in each alternative and find out which expression becomes a multiple of 11?
Now, 4x + 6y = 4 x 5 + 6 = 26
x + y + 4 = 5 + 1 + 4 = 10
9x + 4y = 9 x 5 + 4 = 49
4x – 9y = 4 x 5 -9 = 20 -9 =11
which is divisible by 11
Incorrect
Ans : D
Keeping y =1, for x = 5, we have 3x + 7y =22 which is divisible by 11.
Now, substitute x =5 and y =1 in each alternative and find out which expression becomes a multiple of 11?
Now, 4x + 6y = 4 x 5 + 6 = 26
x + y + 4 = 5 + 1 + 4 = 10
9x + 4y = 9 x 5 + 4 = 49
4x – 9y = 4 x 5 -9 = 20 -9 =11
which is divisible by 11
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Question 2 of 5
2. Question
What is the rightmost integer of the expression 65776759 + 54697467
Correct
Ans: D
Last digit for the power of 6 is 6 (always)
Power cycle of 7 is 7, 9, 3, 1.
Now 467/4 gives a remainder of 3
Then the last digit is 73 = 3
Last digit is 6 + 3 = 9
Incorrect
Ans: D
Last digit for the power of 6 is 6 (always)
Power cycle of 7 is 7, 9, 3, 1.
Now 467/4 gives a remainder of 3
Then the last digit is 73 = 3
Last digit is 6 + 3 = 9
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Question 3 of 5
3. Question
The smallest value of n, for which 2n+1 is not a prime number, is
Correct
Ans: B
(2×1 + 1) = 3.
(2×2 + 1) = 5.
(2×3 + 1) = 7.
(2×4 + 1) = 9.
which is not prime , n=4.
Incorrect
Ans: B
(2×1 + 1) = 3.
(2×2 + 1) = 5.
(2×3 + 1) = 7.
(2×4 + 1) = 9.
which is not prime , n=4.
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Question 4 of 5
4. Question
The largest natural number which exactly divides the product of any four consecutive natural numbers is:
Correct
Ans: C
Required numbers; 1×2×3×4 = 24, which is divisible by 24.
also checking 5 x 6 x 7 x 8 = 1680, which is also divisible by 24.
Incorrect
Ans: C
Required numbers; 1×2×3×4 = 24, which is divisible by 24.
also checking 5 x 6 x 7 x 8 = 1680, which is also divisible by 24.
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Question 5 of 5
5. Question
The digit in unit’s place of the product 71 × 72 × ….. × 79 is
Correct
Ans : A
Required digit = Unit digit
=(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9) = 0.Incorrect
Ans : A
Required digit = Unit digit
=(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9) = 0.
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