Classical

Numbers & Algebra - Numbers and Algebra MCQ

31:  

Which of the following is true?

A.

√2+√5=√7

B.

√2+√5 ≤ √7

C.

√2+√5<√7

D.

√2+√5 > √7

 
 

Option: D

Explanation :

(√2+√5)² = 2 + 2√10 +5 =7+2√10
(√7)² = 7
∴ √2+√5> 7
Alternatively:
√2 > √1 and √5 > √4
∴ √2+√5 > 2+1 
=> √2 + √5 > 3 and √7 < √9 = 3
=> √7 < 3. 
so √2 + √5>√7


32:  

What is the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder?

A.

2987

B.

3601

C.

3600

D.

2986

 
 

Option: B

Explanation :

L.C.M. of 5, 6, 8, 9 and 12 is 360
Required number = 360 K + 1 = (13 x 27 + 9) K + 1
= (13 x 27) K + (9K + 1)
Now this number must be divisible by 13 K = 10 and required number = 3601.


33:  

Average marks of 15 students in a class is 145, maximum marks being 150. If two lowest scores are removed, the average increases by 5. Also, two lowest scores are consecutive multiples of 9. What is lowest score in the.class?

A.

126

B.

117

C.

108

D.

None of these

 
 

Option: C

Explanation :

Total marks of 15 students = 15 x 145 = 2175.
Average marks of 15 students (excluding two lowest scores) = 13 x (145 + 5) = 1950.
∴ Total of two lowest scores = 2175 1950 = 225
Given that two scores are consecutive multiples of 9 * 9x + 9x + 9 = 225 18x = 216
=> 18/x = 216 => x = 216/18
Lowest score = 9x = (216/18) x 9 = 108


34:  

A gardener had a number of shrubs to plant in horizontal rows. At first he tried to plant 5 shrubs in each row, then 6, then 8 and then 12, but had always 1 left. On trying 13, in one row he had none left. What is the smallest number of shrubs that he could have had?

A.

481

B.

477

C.

468

D.

121

 
 

Option: A

Explanation :

Number is 120K + 1= ((13 * 9 + 3) K + 1) 
= 13 * 9K + 3 K + 1, which is divisible by 13.
3K + 1 is divisible by 13.
 ∴  K = 4. Number = 481


35:  

Average age of a team of 15 employees is 36. Youngest of them is 20 years old and eldest is 56 years old. Two of them with average age 28 leave the team. If one of the two comes back on the condition that he will be made the team leader, then which of the following can possibly be average age of the new team so formed?

A.

35

B.

36

C.

38

D.

39

 
 

Option: B

Explanation :

Total age = 15 x 36
After two left, total age = 15 x 36 - 2 x 28 = 540 - 56 = 484 years.
Let the age of the person who returns be x years.
Then new average = (484 +x) / 14
Now x lies between 20 and 36 (both inclusive)
New average min = (484 + 20) /14 = 36 years
And New average max = (484 +36)/14 = 520/14 = 37.14. years




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