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- Question
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Options- A. 1
- B. 2
- C. 3
- D. 4
- Correct Answer
- 2
Explanation
Let the numbers 13 a and 13 bThen, 13a x 13b = 2028
⟹ ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
- 1. A car travelling with 5⁄7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Options- A.
17 6 km/hr 7 - B. 25 km/hr
- C. 30 km/hr
- D. 35 km/hr Discuss
- 2. The rational number for recurring decimal 0.125125.... is:
Options- A.
63 487 - B.
119 993 - C.
125 999 - D. None of these Discuss
- 3. The diagonal of the floor of a rectangular closet is 7½ feet. The shorter side of the closet is 4½ feet. What is the area of the closet in square feet?
Options- A.
5 1 4 - B.
13 1 2 - C. 27
- D. 37 Discuss
- 4. The perimeter of a rectangle having area equal to 144 cm 2 and sides in the ratio 4 : 9 is
Options- A. 52 cm
- B. 56 cm
- C. 60 cm
- D. 64 cm Discuss
- 5. P and Q are 27 km away. Two trains will having speeds of 24 km/h and 18 km/h respectively starts simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is
Options- A. 126 km
- B. 81 km
- C. 48 km
- D. 36 km Discuss
- 6. The sum of two number is 29 and the difference of their squares is 145. The difference between the number is?
Options- A. 13
- B. 5
- C. 8
- D. 11 Discuss
- 7. The average of 4 consecutive even numbers is 27. What is the greatest number
Options- A. 28
- B. 26
- C. 32
- D. 30 Discuss
- 8. The probability that a man will live 10 more year is 1/4 and the probability that his wife will live 10 more year is 1/3. Then, the probability that none of them will be alive after 10 yr, is?
Options- A. 5/12
- B. 1/2
- C. 7/12
- D. 11/12 Discuss
- 9. Number 1 to 25 are marked on tokens of equals size one on each. A token is drawn at random. Find the probability of getting a number divisible by both 2 and 3?
Options- A. 4/25
- B. 7/25
- C. 2/25
- D. 9/25 Discuss
- 10. The average of numbers 0.64204, 0.64203, 0.64202 and 0.64201 is?
Options- A. 0.64202
- B. 0.64204
- C. 0.642022
- D. 0.642025 Discuss
More questions
Correct Answer: 35 km/hr
Explanation:
| Time taken = 1 hr 40 min 48 sec = 1 hr 40 | 4 | min = 1 | 51 | hrs = | 126 | hrs. |
| 5 | 75 | 75 |
Let the actual speed be x km/hr.
| Then, | 5 | x x | 126 | = 42 |
| 7 | 75 |
| ⟹ x = | ❨ | 42 x 7 x 75 | ❩ | = 35 km/hr. |
| 5 x 126 |
Correct Answer:
| 125 |
| 999 |
Explanation:
| 0.125125... = 0.125 = | 125 |
| 999 |
Correct Answer: 27
Explanation:
| Other side | = |
|
ft | ||||||||||||
| = |
|
ft | |||||||||||||
| = |
|
ft | |||||||||||||
| = | 6 ft. |
∴ Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
Correct Answer: 52 cm
Explanation:
Let l = 4k and b = 9k
Area of rectangle = l x b
144 = 4k x 9k
? k2 = 144/36
? k2 = 4
? k = 2
? l = 8 cm and b = 18 cm
Perimeter of rectangle = 2(l + b)
= 2(8 + 18)
= 2 x 26
= 52 cm
Correct Answer: 81 km
Explanation:
If the trains meet after t h.
Relative speed of train = (24 -18) = 6 km/h
? Distance = 27
? t = 27/6 = 9/2 h
? QR distance travel by train which is travelling at a speed of 18 km/h = 18t = 18 x 9/2 = 81 km
Correct Answer: 5
Explanation:
Let the number be a and b
Then, (a-b) = (a2 - b2) / a+b
= 145/29
= 5
Correct Answer: 30
Explanation:
Let the four consecutive even number are x, ( x+2), (x+4), (x+6).
Clearly this is a series of consecutive even numbers
According to the formula,
Average of consecutive numbers = (first number + last number)/ 2
? 27 = [x + (x + 6)]/2
? x + 3 = 27
? x =24
? Greatest number = 4th consecutive even number = (x + 6) = 24 + 6 = 30
Correct Answer: 1/2
Explanation:
Let the name of the man be A and that of his wife be B. Then ,P(A will not be alive after 10 yr and B will not be alive after 10yr) = 3/4 x 2/3 = 1/2
Correct Answer: 4/25
Explanation:
Total number of ways of selecting one number from 25 number is 25C1 ways.
Let E be the event of drawing a number divisible by both 2 and 3
i.e., (if a number is divisible by both 2 and 3, it is divisible by 6 also)
E = {6, 12, 18, 24}
? Required probability = P(E) = n(E) / n(S) = 4/25
Correct Answer: 0.642025
Explanation:
Average = (0.64204 + 0.64203 + 0.64202 + 0.64201)/ 4
=2.5681/ 4
=0.642025
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