Discussion
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- Question
A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is ?
Options- A. 63
- B. 31
- C. 16
- D. 27
- Correct Answer
- 31
ExplanationTo get the least number of coconuts :
LCM = 30 => 30 + 1 = 31 - 1. If HCF of two numbers is 8,which of the following can never be their LCM?
Options- A. 32
- B. 48
- C. 60
- D. 152 Discuss
- 2. H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 and 16 x 81 x 5 x 11 x 49 is
Options- A. 180
- B. 360
- C. 540
- D. 1260 Discuss
- Prime factorization of 4 × 27 × 3125:
- 4 = 2²
- 27 = 3³
- 3125 = 5?
- Prime factorization of 8 × 9 × 25 × 7:
- 8 = 2³
- 9 = 3²
- 25 = 5²
- 7 = 7¹
- Prime factorization of 16 × 81 × 5 × 11 × 49:
- 16 = 2?
- 81 = 3?
- 5 = 5¹
- 11 = 11¹
- 49 = 7²
- Find the common prime factors and their lowest powers:
- For 2, the lowest power is 2².
- For 3, the lowest power is 3².
- For 5, the lowest power is 5¹.
- For 7, the lowest power is 7? (since 7 is absent in the first number).
- For 11, the lowest power is 11? (since 11 is absent in the first two numbers).
- Calculate the HCF:
- HCF = 2² × 3² × 5¹ = 4 × 9 × 5 = 180.
- Final answer:
The HCF of the given numbers is 180.
- 3. Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500 .The smallest numbers is
Options- A. 4
- B. 5
- C. 6
- D. 10 Discuss
- 4. The H.C.F and L.C.M of two numbers are 11 and 385 respectively. If one number lies between 75 and 125 , then that number is
Options- A. 77
- B. 88
- C. 99
- D. 110 Discuss
- 5. If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Options- A. 55/601
- B. 601/55
- C. 11/120
- D. 120/11 Discuss
- 6. LCM of 80, 85, 90
Options- A. 11440
- B. 11998
- C. 12240
- D. 12880 Discuss
- 7. A drink vendor has 368 liters of Maaza, 80 liters of Pepsi and 144 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required ?
Options- A. 47
- B. 46
- C. 37
- D. 35 Discuss
- 8. The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
Options- A. 91
- B. 910
- C. 1001
- D. 1911 Discuss
- 9. H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 2 4 x 3 5 x 5 2 x 7 2 . What is the third number?
Options- A. 47628
- B. 49874
- C. 24157
- D. 42146 Discuss
- 10. LCD of 12 and 18
Options- A. 36
- B. 42
- C. 12
- D. 6 Discuss
Search Results
Correct Answer: 60
Explanation:
60 is not a multiple of 8
Correct Answer: 180
Explanation:
To find the HCF (Highest Common Factor) of the given numbers, we begin by breaking down each number into its prime factorization. Here are the steps:
Correct Answer: 5
Correct Answer: 77
Explanation:
Product of numbers = 11 x 385 = 4235
Let the numbers be 11a and 11b . Then , 11a x 11b = 4235 => ab = 35
Now, co-primes with product 35 are (1,35) and (5,7)
So, the numbers are ( 11 x 1, 11 x 35) and (11 x 5, 11 x 7)
Since one number lies 75 and 125, the suitable pair is (55,77)
Hence , required number = 77
Correct Answer: 11/120
Explanation:
Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum = = = =
Correct Answer: 12240
Explanation:
LCM of (80, 85, 90) can be found by prime factorizing them.
80 ? 2 × 2 × 2 × 2 × 5
85 ? 17 × 5
90 ? 2 × 3 × 3 × 5
L.C.M of (80,85,90) = 2 × 2 x 2 × 2 × 3 × 3 × 5 × 17
= 16 x 9 x 85
= 144 x 85
= 12240
L.C.M of (80,85,90) = 12240.
Correct Answer: 37
Explanation:
The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 368/16 = 23
Number of cans of Pepsi = 80/16 = 5
Number of cans of Sprite = 144/16 = 9
The total number of cans required = 23 + 5 + 9 = 37 cans.
Correct Answer: 91
Explanation:
Required number of students = H.C.F of 1001 and 910 = 91
Correct Answer: 47628
Correct Answer: 36
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