Numbers problems
- 1. How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options- A. 4
- B. 5
- C. 6
- D. 7 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 4
Explanation:
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 → 11,3,4 (/)
396 → 11,3,4 (/)
462 → 11,3 (X)
792 → 11,3,4 (/)
968 → 11,4 (X)
2178 → 11,3 (X)
5184 → 3,4 (X)
6336 → 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
- 2. n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
Options- A. 3
- B. 2
- C. 1
- D. 0 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 2
Explanation:
Let n = 4 q + 3. Then 2 n = 8 q + 6 = 4(2 q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
- 3. The largest 4 digit number exactly divisible by 88 is ?
Options- A. 9944
- B. 9768
- C. 8888
- D. 9988 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk
Correct Answer: 9944
Explanation:
The largest 4 digit number is = 9999
After dividing 9999 with 88, we get 55 as remainder
so largest 4 digit number divisible by 88 = 9999-55 = 9944.
- 4. How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?
Options- A. 7
- B. 9
- C. 11
- D. 5 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 9
Explanation:
LCM of 2, 3, 7 is 42.
=> (700 ? 300)/42 = 9 22/42 => 9 Numbers.
- 5. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x+y is equal to ?
Options- A. 5
- B. 4
- C. 3
- D. 2 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 2
Explanation:
Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.
- 6. About 4 out of 5 students are left handed. If there are totally 40 students in an class. How many would be left handed ?
Options- A. 40
- B. 45
- C. 32
- D. 30 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank PO
Correct Answer: 32
Explanation:
Probability of left handed = 4/5
total student = 40
total left handed = 40 x(4/5)
= 32
- 7. What will come in place of the question mark (?) in the following questions ? 22% of ? + 166.64 = 340
Options- A. 788
- B. 786
- C. 784
- D. 792 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk
Correct Answer: 788
Explanation:
(kx22)/100 = 340 - 166.64 = 173.36
k = (173.36 x 100)/22
k = 788
- 8. The sum of three consecutive odd numbers is 93. What is the middle number?
Options- A. 31
- B. 33
- C. 29
- D. 27 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 31
Explanation:
Let the three consecutive odd numbers be x, x+2, x+4
Then,
x + x + 2 + x + 4 = 93
=> 3x + 6 = 93
=> 3x = 87
=> x = 29 => 29, 31, 33 are three consecutive odd numbers.
Therefore, the middle number is 31.
- 9. The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?
Options- A. 80 degrees
- B. 60 degrees
- C. 120 degrees
- D. 40 degrees Also asked in: AIEEE, Bank Exams, GRE, TOEFL, Bank Clerk
Correct Answer: 60 degrees
Explanation:
Given the angles of a quadrilateral are in the ratio of 2:4:7:5
Let the angles of a quadrilateral are 2x, 4x, 7x, 5x
But we know that sum of the angles = 360 degrees.
=> 2x + 4x + 7x + 5x = 360
=> x = 20
Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.
One of the angle of the triangle = 2 x 40 = 80 degrees
The other angle is 180 - (40 + 80) = 60 degrees.
Hence the second largest angle of the triangle is 60 degrees.
- 10. If x is a whole number, then x²(x² - 1) is always divisible by ?
Options- A. 4
- B. 8
- C. 12
- D. None Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 12
Explanation:
we can do this by trial and error method.
Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.
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