Number System problems
- 1. Of the three numbers, the sum of first two is 45, the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. The third number is?
Options- A. 20
- B. 25
- C. 30
- D. 35 Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 30
Explanation:
Let the number be x, y, z
Then,
x + y = 45,
y + z = 55,
z + 3x = 30
Now, y = (45 - x) and
z = 55 - y
? z = 55 - (45 - x ) = 10 + x
? 10 + x + 3x = 90
? x = 20
So, third number = z
= 10 + x = 30
- 2. A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?
Options- A. 9
- B. 3
- C. 1
- D. 4 Discuss
Correct Answer: 4
Explanation:
The number is of the form (5x + 3 ) where x is an integer
? [(5x + 3)2] / 5 = ( 25x2 + 30x + 9) / 5
= 25x2/ 5 + 30x/5 + (5 +4)/5
? The remainder is 4.
- 3. In a question divisor is 2/3 of the dividend and 2 times the remainder. If the remainder is 5, find the dividend.?
Options- A. 15
- B. 25
- C. 18
- D. 24 Discuss
Correct Answer: 15
Explanation:
According to the question
Divisor = 2/3 x dividend
and Divisor = 2 x remainder
or 2/3 x dividend = 2 x 5
? Dividend = 2 x 5 x 3 / 2 = 15
- 4. How many figures (digits) are required to number a book containing 200 pages?
Options- A. 200
- B. 600
- C. 492
- D. 372 Discuss
Correct Answer: 492
Explanation:
Number of one digit pages from
1 to 9 = 9
Number of two digit pages from
10 to 99 = 90
Number of three digit pages from
100 to 200 = 101
? Total number of required figures
= 9 x 1 + 90 x 2 + 101 x 3 = 492
- 5. The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1, If the sum of the digits of the number is seven, then what is the number?
Options- A. 52
- B. 16
- C. 34
- D. Data in inadequate Discuss
Correct Answer: 52
Explanation:
Let 1/2 of the no. = 10x + y
and the no. = 10v + w
From the given conditions,
w= x and v = y-1
Thus the no. = 10 (y-1) + x
? 2(10x + y ) = 10 (y-1) + x
? 8y - 19x = 10 ...(i)
v + w = 7
? y-1 + x = 7
? x + y = 8
Solving equations (i) and (ii) , we get
x = 2 and y = 6
? From equations (A)
Number = 10 (y - 1) + x = 52.
- 6. A two-digit number is seven times the sum of its digits, If each digit is increased by 2, the number thus obtained is 4 more than six times the sum of its digits, Find the number?
Options- A. 42
- B. 24
- C. 48
- D. Data adequate Discuss
Correct Answer: 42
Explanation:
Let the two-digit number be 10x + y
10x + y = 7(x + y)
? x = 2y ...(i)
10(x +2 ) + (y + 2) = 6(x + y + 4) + 4
or 10x + y + 22 = 6x + 6y + 28
? 4x - 5y = 6 ...(ii)
Solving equations (i) and (ii)
We get x = 4 and y = 2
- 7. If a number is decreased by 4 and divided by 6 the result is 9. What would be the result if 3 is subtracted from the number and then it is divided by 5?
Options- A. 9 2/ 5
- B. 10 1/ 5
- C. 11 2/ 5
- D. 11 Discuss
Correct Answer: 11
Explanation:
Let the number be x.
? (x - 4)/6 = 9
? x = 58
Again (x - 3)/5 = (58 - 3)/5 = 11
- 8. The numbers x, y, z are such that xy = 96050 and xz = 95625 and y is greater than z by one. Find out the number z?
Options- A. 425
- B. 220
- C. 525
- D. 225 Discuss
Correct Answer: 225
Explanation:
xy = 96050 ...(i)
and xz = 95625 ...(ii)
and y - z = 1 ... (iii)
Dividing (i) by (ii) we get
y/z = 96050 / 95625
= 3842 / 3825
= 226 / 225 ... (iv)
Combining (iii) and (iv) we get z = 225.
- 9. The ratio of two number is 3:2, If 10 and the sum of the two numbers are added to their product, square of sixteen is obtained. What could be the smaller number?
Options- A. 14
- B. 12
- C. 16
- D. 18 Discuss
Correct Answer: 12
Explanation:
Let the two numbers be 3N and 2N
According to the question.
10 + (3N +2N ) + (3N x 2N) = 162
? 6N2 + 5N - 246 = 0
? 6N2 + 41N - 36N - 246 = 0
? N(6N + 41 ) - 6(6N + 41) = 0
? (6N + 41 ) (N - 6) = 0
? N = 6 or -41/6 (But -ve value cannot be accepted )
? Smaller number = 2N = 2 x 6 = 12 .
- 10. In a two digit number, the digital unit place is 1 more than twice of the digit at ten's place. If the digit at unit's and ten's place be interchanged, then the difference between the new number and original number is less than 1 to that of original number. what is the original number?
Options- A. 52
- B. 73
- C. 25
- D. 37 Discuss
Correct Answer: 37
Explanation:
Let the original number be 10p + q.
So from question,
q = 2p + 1 ...(i)
and (10q + p) - (10p + q ) = (10p + q) - 1
? 9q - 9p = 10p + q -1
? 19p - 8q = 1...(ii)
Putting the value of (i) in equation (ii) we get
19p - 8(2p + 1) = 1
? 19p - 16p - 8 = 1
? 3p = 9
? p = 3
So, q = 2 x 3 + 1 = 7
? Original number = 10 x 3 + 7 = 37
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