Numbers problems
- 1. 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 Discuss
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.
- 2. If V = 12R / (r + R) , then R =
Options- A. Vr / (12 - V)
- B. Vr + (V /12 )
- C. V
- D. V / (r - 12 ) Discuss
Correct Answer: Vr / (12 - V)
Explanation:
We have to rearrange the equation to make R the subject.
Start by cross multiplying by (r + R); V (r + R) = 12R
Multiply out the bracket Vr + VR = 12R
- 3. If x is a whole number, then x²(x² - 1) is always divisible by ?
Options- A. 4
- B. 8
- C. 12
- D. None Discuss
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.
- 4. Find the number of factors of 9321 ?
Options- A. 4
- B. 5
- C. 7
- D. 8 Discuss
Correct Answer: 8
Explanation:
9321 = 3 x 13 x 239 = 31 x 13 1 x 239 1 ; add one to all the powers ie.,
(1+1) x (1+1) x (1+1)= 8 ;
we get eight factors.
- 5. The product of a number and its multiplicative inverse is
Options- A. 1
- B. 0
- C. -1
- D. Infinity Discuss
Correct Answer: 1
Explanation:
The mutiplicative inverse of a number is nothing but a reciprocal of a number.
Now, the product of a number and its multiplicative inverse is always equal to 1.
For example :
Let the number be 15
Multiplicative inverse of 15 = 1/15
The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.
- 6. 3131×31-27 =?
Options- A. 961 x 861
- B. 961 x 961
- C. 961 x 2
- D. 29791 Discuss
Correct Answer: 961 x 961
Explanation:
We know that
= = 961 x 961.
- 7. What is the remainder when 1523+2323 is divided by 19 ?
Options- A. 4
- B. 3
- C. 1
- D. 0 Discuss
Correct Answer: 0
Explanation:
The remainder on dividing by 19 will be = 0.
- 8. Find the next number in the series 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20,...
Options- A. 27
- B. 26
- C. 24
- D. 25 Discuss
Correct Answer: 26
Explanation:
The pattern is three consecutive numbers and then three consecutive numbers missing.Then four consecutive numbers and then four consecutive numbers missing.Then five consecutive numbers and then five consecutive numbers missing.
The next number=20+6=26
- 9. Find the next number in the series 141,137,146,130,155,119,...
Options- A. 147
- B. 168
- C. 162
- D. 182 Discuss
Correct Answer: 168
Explanation:
The pattern is -4, +9,-16, +25, -36
The next number=119+49=168
- 10. In a triangle ABC, angle 'a' is the smallest one & A+7B = 112. Find the range of value 'c' ?
Options- A. 138 to 164
- B. 125 to 147
- C. 148 to 158
- D. 152 to 164 Discuss
Correct Answer: 152 to 164
Explanation:
A+7B=112
it is clear that A = 14, then it becomes A>=B, but A is smallest angle) given
so, range of A is 0.0001 to 13.9999 ( I am taking upto 4 decimal places)
so, range of B becomes 14 to 16 ( after rounding off to 4 decimal places)
so, range of C becomes 152 to 164 ( after rounding off to 4 decimal places)
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