Number System problems
- 1. A number consists of two digits. The sum of the digit is 10. On reversing the digits of the number, the number decreases by 36. What is the product of the two digits?
Options- A. 21
- B. 24
- C. 36
- D. 42 Discuss
Correct Answer: 21
Explanation:
Let the unit digits of the number be N and 10s digit be M
? Number = 10M + N
According to the question
MN = 10 .......(i)
And 10N + M = (10M + N) - 36
? 10N + M - 10M - N = -36
? 9N - 9M = - 36
? N - M = -4 .......(2)
On Adding eq. (i) and (ii) we get
N + M = 10
N - M = - 4
2N = 6
? N = 3 and M = 7
? Required product of two digits = 3 x 7 = 21
- 2. The sum of 5 consecutive odd numbers is 190. What is the sum of the largest and the smallest numbers?
Options- A. 75
- B. 77
- C. 76
- D. 73 Discuss
Correct Answer: 76
Explanation:
Let the five consecutive number are N - 2, N - 1, N, N +1, N+2
Sum of numbers = 190
? N-2 + N -1 + N + N + 2 = 190
? 5N = 190
? N = 38
Sum of largest and smallest numbers = (N + 2) + (N - 2)
= 2N = 2 x 38
= 76
- 3. If a =16 and b= 5, the value of (a 2+ b 2+ ab) / (a 3 - b 3) is?
Options- A. 1/11
- B. 1/19
- C. 121/3971
- D. None of these Discuss
Correct Answer: 1/11
Explanation:
Given Exp. = (a2+ b2+ ab) / (a3-b3)
= 1 / (a - b)
= 1 / (16 - 5)
= 1/11.
- 4. Five time of a position integer is equal to 3 less then twice the square of that number. Find the number.
Options- A. 3
- B. 13
- C. 23
- D. 33 Discuss
Correct Answer: 3
Explanation:
Let the number be N
According to the question 5N = 2N2 - 3
? 2N2 - 5N -3 = 0
? (N - 3) (2N + 1) = 0
N = 3 & -1/2
Thus the required number is 3
- 5. A student was asked to multiply a number by 3/2 but he divided that number by 3/2. The result was therefore 10 less then the correct answer. Find the number.
Options- A. 10
- B. 12
- C. 15
- D. 20 Discuss
Correct Answer: 12
Explanation:
Let the number be N
According to the question,
[N x (3/2)] - [N / (3/2)] =10
? 3N/2 - 2N/3 = 10
? (9N - 4N)/6 = 10
? 5N / 6 = 10
? N = (10 x 6)/5 =12
- 6. The sum of five consecutive odd number is equal to 175. What is the sum of the second large number and the square of the smallest number among them together?
Options- A. 989
- B. 997
- C. 979
- D. none of the above Discuss
Correct Answer: none of the above
Explanation:
Sum of the five consecutive odd number = N + (N + 2) + (N + 4) + (N + 6) + (N + 8) =175
? 5N + 20 =175
? N = (175 - 20) / 5 = 31
Sum of the second largest and square of smallest one = (31 + 6) + (31)2
= 37 + 961=998
- 7. On children day sweet were to be equally distributed among 300 children. But on that particular day 50 children remain absent hence each child got one extra sweet. How many sweet were distributed?
Options- A. 1450
- B. 1700
- C. 1500
- D. 1650 Discuss
Correct Answer: 1500
Explanation:
let the total number of sweet = N
According to the question
(N/250) - (N/300) = 1
? (6N - 5N) / 1500=1
? N = 1500
- 8. The sum of the two position number P and Q is 2.5 time their difference .If the product of the number 84 then the what is the sum of those two number?
Options- A. 26
- B. 24
- C. 22
- D. 20 Discuss
Correct Answer: 20
Explanation:
Let the number be P and Q
According to the question
(P + Q) = 2.5 (P - Q)
? P + Q = 2.5P - 25Q
? 3.5Q = 1.5P
? P / Q = 7/3 .....(i)
Now PQ = 84
? Q2 = (84 x 3) / 7
? Q2 = 36
? Q = 6
&ther4; P = (7/3) x 6 = 14
Sum of the number = P + Q = 14 + 6 = 20
- 9. Out of three given number the first number is twice the second and thrice number is 154 then what is the difference between the first and third number?
Options- A. 126
- B. 42
- C. 168
- D. 52 Discuss
Correct Answer: 168
Explanation:
Let the third number = N
Then the first number = 3N
And second number = 3N/2
According to the question [N + 3N + 3N/2] / 3=154
? (2N +6N +3N) / 6 = 154
? N = (154 x 6) / 11 = 84
? Required difference = 3N - N = 2N
= 2 x 84 = 168
- 10. Find the maximum number of tree which can plant 20 m apart on the two side of straight road 1760 m long
Options- A. 174
- B. 176
- C. 180
- D. 178 Discuss
Correct Answer: 178
Explanation:
Number of trees that can be planted on one side of road = (1760 / 20) + 1
= 88 + 1
=89
? Trees on the both side = 2 x 89=178
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