TOPIC :Problems On Numbers
Total no. of question: 10
level: average
Q. 1. If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
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Let the number be 100 %
find 3/10 ??? i.e = we have to calculate 30%
given, 1/3 of 25%= 15
therefore 25% =45
So, 30%=54
find 3/10 ??? i.e = we have to calculate 30%
given, 1/3 of 25%= 15
therefore 25% =45
So, 30%=54
Q.2. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
A. 9
B. 11
C. 13
D. 15
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Answer: Option D
Explanation:
Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15.
Q.3. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
A. 3
B. 4
C. 9
D. Cannot be determined
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Answer: Option B
Explanation:
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Q 4. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
A. 20
B. 30
C. 40
D. None of these
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Answer: Option A
Explanation:
Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20.
Q 5. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
A. 3
B. 10
C. 17
D. 20
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Answer: Option A
Explanation:
Let the number be x.
Then, x + 17 = 60/x
x^2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3.
Q 6. What is the sum of two consecutive even numbers, the difference of whose squares is 84?
A. 34
B. 38
C. 42
D. 46
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Answer: Option C
Explanation:
Let the numbers be x and x + 2.
Then, (x + 2)^2 - x^2 = 84
4x + 4 = 84
4x = 80
x = 20.
The required sum = x + (x + 2) = 2x + 2 = 42.
Q 7. 1397 x 1397 = ?
A. 1951609
B. 1981709
C. 18362619
D. 2031719
E. None of these
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Answer: Option A
Explanation:
1397 x 1397 = (1397)^2
= (1400 - 3)^2
= (1400)^2 + (3)^2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Q 8. Which of the following numbers will completely divide (4915 - 1) ?
A. 8
B. 14
C. 46
D. 50
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Answer: Option A
Explanation:
(xn - 1) will be divisibly by (x + 1) only when n is even.
(4915 - 1) = {(7^2)^15 - 1} = (7^30 - 1), which is divisible by (7 +1), i.e., 8.
Q 9 On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
A. 10
B. 11
C. 12
D. 13
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Answer: Option A
Explanation:
Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
The required 3-digit number is 127, the sum of whose digits is 10.
Q 10. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
A. 69
B. 78
C. 96
D. Cannot be determined
E. None of these
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Answer: Option D
Explanation:
Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69.
Hence, the number cannot be determined.
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