Problems on Numbers
- 1. A fraction becomes 2/3 when 1 is added to both, its numerator and denominator. And, it becomes 1/2 when 1 is subtracted from both the numerator and denominator. What is the fraction?
Options- A. 1/3
- B. 4/5
- C. 3/5
- D. 2/5 Discuss
Correct Answer: 3/5
Explanation:
Let the required fraction be x/y. Then, x+1 / y+1 = 2 / 3 => 3x – 2y = - 1 …(i) and x – 1 / y – 1 = 1 / 2 2x – y = 1 …(ii) Solving (i) and (ii), x = 3 , y = 5 therefore, Required fraction= 3/5
- 2. There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number ?
Options- A. 17
- B. 19
- C. 13
- D. 11 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 13
Explanation:
(385/1001) = 5/13
First Number is 5
=> Fourth number is 13
- 3. 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Options- A. 24
- B. 34
- C. 44
- D. 54 Discuss
Correct Answer: 34
Explanation:
Let the two parts be (54 - x) and x.
Then, 10 (54 - x) + 22x = 780
=> 12x = 240
=> x = 20.
Bigger part = (54 - x) = 34.
- 4. Find the number which when multiplied by 15 is increased by 196.
Options- A. 10
- B. 12
- C. 14
- D. 16 Discuss
Correct Answer: 14
Explanation:
Let the number be x. Then, 15x - x = 196 <=> 14x = 196 => x = 14..
- 5. The sum of the squares of two numbers is 3341 and the diference of their squares is 891. The numbers are :
Options- A. 35 and 46
- B. 35 and 50
- C. 40 and 55
- D. 45 and 60 Discuss
Correct Answer: 35 and 46
Explanation:
Let the numbers be x and y. Then,
x^2+y^2=3341......(1)
x^2-y^2=891......(2)
Adding (i) and (ii), we get : 2x^2=4232 or x^2= 2116 or x =46
Subtracting (ii) from (i), we get : 2y^2= 2450 or y^2 = 1225 or y = 35
So, the numbers are 35 and 46
- 6. A number is 2 more than thrice the second number and 4 times the smaller number is 5 more than the greater number. What is greater number ?
Options- A. 7
- B. 23
- C. 9
- D. 21 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 23
Explanation:
Let the greater and smaller number be p and q respectively.
4q = p + 5 ------ (I)
p = 3q+2 ------- (II)
From equation (I) and (II)
q = 7
p = 23
- 7. On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is ?
Options- A. 476190476
- B. 48617
- C. 47619
- D. 4587962 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 47619
Explanation:
By hit and trail, we find that
47619 x 7 = 333333.
7) 333333 (47619
333333
----------------
0
And 476190476 x 7 = 3333333333 but smallest number is 47619.
- 8. How many numbers up to 101 and 300 are divisible by 11 ?
Options- A. 18
- B. 20
- C. 19
- D. 17 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 18
Explanation:
(300 ? 101)/11 = 199/11 = 18 1/11
18 Numbers.
- 9. Sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
Options- A. 11 and 4
- B. 3 and 11
- C. 11 and 33
- D. 40 and 4 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 11 and 33
Explanation:
Let the smaller number be 'm'
Then, from the given data, the larger number is '3m'
Given that m + 3m = 44
=> 4m = 44
m = 44/4 = 11
=> m = 11
=> 3m = 3 x 11 = 33
Hence, the two numbers are 11 and 33.
- 10. If the product of 6 integers is negative, at most how many of the integers can be negative?
Options- A. 2
- B. 3
- C. 4
- D. 5 Also asked in: GRE
Correct Answer: 5
Explanation:
Multiplying two negatives (or any even multiple) results in a positive. But multiplying three negatives (or any odd multiple) gives a negative. If the result of multiplying 6 negatives is odd, the largest number of negative integers will be the largest odd number (i.e.5)
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