CAT 2019 - Slot 2 - Quantitative eAptituteThe salaries of Ramesh, Ganesh and Rajesh were in the ratio 6:5:7 in 2010

Q. 1: The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6:5:7 in 2010, and in the ratio 3:4:3 in 2015. If Ramesh’s salary increased by 25% during 2010- 2015, then the percentage increase in Rajesh’s salary during this period is closest to
1. 7
2. 9
3. 10
4. 8

 Let us say that the salaries of Ramesh, Ganesh, and Rajesh were 60, 50, 70 in 2010.

In 2015, Ramesh’s salary became 60*1.25 = 75.

In 2015, Rajesh’s salary was same as Ramesh.

So, %increase in Rajesh’s salary = 5/70 * 100 = 7.14%

 

Q. 2: If x is real number, then   is a real number if and only if?
1. 1≤x≤2
2. -3≤x≤3
3. -1≤x≤3
4. 1≤x≤3

As we know that any value under square root must be greater than 0 . So

Log(base e) 4x-x^2/3 ≥ 0

So, 4x-x^2/3≥ 1

x^2-4x +3 ≤ 0

On solving, we get

S belongs to [1,3]

Q. 3: In an examination, Rama’s score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:3. Then Anjali’s score exceeded Rama’s score by
1. 24
2. 26
3. 35
4. 32 

Let score of Rama = r, mohan = m and Anjali = a

As score was one-twelfth of the sum of the scores of Mohan and Anjali.

So 12r = m + a……(1)

Similarly after score of each of them increased by 6, score of scores of Anjali, Mohan, and Rama

Becomes in the ratio 11 : 10 :3

Let 11k = r+6, m+6 = 10k and a+6 = 3k, putting values of the 3 in equation 1, we get

a – r = 40 – 8 = 32

 

Q. 4:  How many pairs (m, n) of positive integer satisfy the equation m^2+105=n^2 ?

given m^2 + 105 = n^2

n^2 – m^2 = 105

(n-m) * (n+m) = 105

105 can be written as 105*1 = 21*5 = 15*7 = 35*3

So, only 4 cases possible to get values of n, m as positive. Thus number of solution = 4

Q. 5: Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?
1. 13
2. 12
3. 15
4. 14

In 3 days, Anil does 3/20 of work

Let a and s work for x days, then total work done = 3x/40

So, 3/20 + 3x/40 = 9/10

15/20 = 3x/40

X = 10

So, total no. of days = 13

 

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