02-08-2021 Answers

1. Among how many students, can 175 bananas and 105 apples can be equally divided?

Answer: 7

Solution: HCF of 175 and 105 = 35.

35 = 5*7.

So the fruits can be divided equally among 5 or 7 or 35 students.

Among the given options 7 is the answer.


2. The LCM and HCF of two numbers are 2400 and 16. One of the numbers is 480. The other number is

Answer: 80

Solution: Product of two numbers = Product of their LCM and HCF

Other number = (2400*16)/480 = 80


3. The LCM of three numbers is 4752 and HCF is 6. If two numbers are 48 and 66, find the third least possible number

Answer: 54

Solution: Let the third number be 6x.

48 = 6*8 and 66 = 6*11

4752  = 6*8*11*x, solving x=9

So the number = 6x = 54


4. Find the LCM of 2.2, 540 and 1.08.

Answer: 594

Solution: LCM of 22,540,108 is 5940

Here minimum decimal place is 1 (in 2.2)

Hence the LCM is 594


5. If the product of two numbers is same as LCM, then which of the following two options can be true?

Answer: Both the numbers are prime, Both the numbers are co-prime

Solution: Product of two numbers = Product of their LCM*HCF. This implies in the given scenario HCF must be 1.

So the mentioned case occurs when ever

1. Both the numbers are prime (Example 5 and 7)

2. One of the numbers is prime and the other is not a multiple of that  prime (That is coprime) (Example 7 and 6)


6. The LCM of first 70 natural numbers is N. What is the LCM of first 75 natural numbers?

Answer: 5183N

Solution: The prime numbers between 71 and 75 inclusive are 71 and 73

Hence required LCM = N * 71 * 73 = 5183N


7. Find the two numbers whose L. C. M. is 1188 and H. C. F. is 9

Answer: 27, 396

Solution: Product of two numbers = HCF * LCM = 1188 * 9 = 10692

Only 27*396 = 10692 and hence the numbers are 27 and 396


8. What must be subtracted from 3687 so that it becomes divisible by both 5 and 7?

Answer: 12

Solution: LCM of 5 & 7 is 35.

3687 mod 35 = 12 which is the desired answer

Note: 3687 mod 35 means remainder when 3687 is divided by 35


9. Find the largest number which leaves the same remainder when it divides 444, 804 and 1344.

Answer: 180

Solution: Reqd number = HCF of (1344-804) and (804-444)

= HCF of 540 and 360

= 180


10. Find the maximum number of boys among whom 429 apples and 715 berries can be equally distributed.

Answer: 143

Solution: Required number of boys = HCF of 429 and 715 = 143


11. The LCM and HCF of two numbers are 630 and 9. If the sum of the numbers is 153, their difference is

Answer: 27

Solution: Product of two numbers = Product of their LCM and HCF

Let the numbers be a,b.

ab = 630*9

a+b=153

Using the formula (a-b)^2 = (a+b)^2 - 4ab,

(a-b)^2 = 153^2 - 4*630*9,

Solving a-b = 27


12. Four bells first begin to toll together and then at intervals of 6, 7, 8 and 9 seconds respectively. Find how many times the bells toll together in two hours.

Answer: 14 times

Solution: LCM of 6, 7, 8, 9 = 504

Therefore, all the bells  toll together for every 504 seconds.

Hence in two hours, number of times they toll together = (2*60*60)/504 = 14 times (rounded to the integral value)


13. In an airforce of a country, there are (3x^2-5x-2) fighter planes and (x^2-x-2) cargo planes. Both types of planes are put in different group in such a way that every group consists of equal number of planes. An official is appointed to take care of each and every group. Find out the least number of officials to be appointed so that there is atleast one official for every group.

Answer: x-2

Solution: The required answer is nothing but HCF of both equations.

3x^2-5x-2 = (x-2)(3x+1)

x^2-x-2 = (x-2)(x+1)

Hence HCF is x-2


14. The LCM of 19+x and 51+x is 420. Find x.

Answer: 9

Solution: Solve this by going through the options (substituting options one by one)

Only x=9 satisfies the criteria


15. The smallest five digit number which is exactly divisible by 12, 15 and 18 is

Answer: 10080

Solution: LCM of 12,15 and 18 = 180.

10000 mod 180 = 100.

Hence required number = 10000 + (180-100) = 10080


16. Which of the following is a pair of co-primes?

Answer: (18, 25)

Solution: Co-Primes have 1 as their HCF


17. The LCM of two numbers is 280 and their ratio is 7:8. The sum of the two numbers is

Answer: 75

Solution: Let the numbers be 7x and 8x.

7*8*x=280, x=5.

Sum = 7x+8x = 15x = 15*5 = 75


18. What is the smallest number which when increased by 5 is completely divisible by 8,11 and 24 ?

Answer: 259

Solution: LCM of 8,11,24 = 264

Hence reqd number = 264-5 = 259


19. 294 blue balls, 252 pink balls and 215 yellow balls are distributed equally among some students with 5 yellow balls left over. What is the biggest possible number of students?

Answer: 42

Solution: Biggest possible number of students = HCF of 294, 252 and 210(215-5)  {As 5 yellow balls were left).

HCF of 294, 252 and 210 is 42.


20. Sum of two positive integers is 85. What can be the maximum possible LCM of these numbers?

Answer: 1806

Solution: For the LCM to be maximum the numbers have to be maximum and should be closer to each other.

85/2 = 42.5

The closer coprimes which add upto 85 are 42 and 43.

Hence LCM = 42*43 = 1806

Comments

Post a Comment

Popular posts from this blog

16-01-2022 Answers

 1. Ajay and Manoj start in bike at the same time from their homes which are 45 kms apart. If one moves west at 50 kmph and the other moves east at 40 kmph, what will be the distance between them after 2 hours? Answer: 225 kms Solution: Initial distance = 45 km As they are moving in two opposite directions so relative speed = 50 + 40 = 90 kmph. Distance between them after 2 hours = 45 +(90*2) = 225 kms. 2. Krish is the brother-in-law of Kamini. Kirmani is the father of Kishore. Kishore is the spouse of Kamini. How is Krish related to Kishore ? Answer: Brother Solution: "Brother in law" means "The brother of one's husband or wife". Spouse means "partner in a marriage" So Krish is the brother of Kishore. 3. Answer the four questions given below based on the information provided. Four sisters - Suvarna, Tara, Uma and Vibha are playing a game where the loser doubles the money of each of the other players from her share. They played four games and each of t...
Read more

17-01-2022 Answers

Image
 1. Choose the odd pair. Answer: Infer/Deduce Chaos/Order Vice/Virtue Fact/Fiction Solution: Other pairs are opposite to each other while infer and deduce have a similar meaning. 2. How many 6's are there in the following number series which are either preceded by 4 or followed by 7? 3 1 2 9 6 4 7 6 4 6 7 2 9 7 6 4 4 6 7 Answer: Two 3. Which is the next letter in the following series? A, B, E, C, L, R, N, ? Answer: G Solution: Alphabet in odd position is made of only straight lines. In even position it must be made of atleast one curved line. Hence G is the answer. 4. A Guarantee is a promise or assurance that attests to the quality of a product that is either (1) given in writing by the manufacturer or (2) given verbally by the person selling the product. Which situation below is the best example of a Guarantee? Answer: Dorin buys a used laptop from her coworker who says that she will refund Dorin's money if the laptop's performance is not of the highest quality. Solution:...
Read more

19/01/2022 Answer

1. Choose the option which is similar in meaning to the highlighted word. She was conspicuous by her absence in the meeting held yesterday. Answer: apparent 2. Choose the antonym of the given word Adulterate Answer: Purify 3. The jumbled letters of a meaningful word are given below. Rearrange the letters to form the meaningful word and then select the option which is almost similar in meaning to the word. DAXEPN Answer: INCREASE Solution: The word is EXPAND which means INCREASE 4. Choose the part of the sentence that has error in it.  After she returned from the three-week vacation, she looked very well. Answer: she looked very well. Solution: The correct sentence is " After she returned from the three-week vacation, she looked very good." 5. Choose the option to replace the phrase highlighted to make the sentence grammatically correct. If the sentence is correct as it is, choose "No correction required" The performance of our players was rather worst than I had exp...
Read more