CMAT 4th May 2023 Slot-1

It is given,

Number of players who scored less than or equal to 40 runs in tournament Q = 300 - 90 = 210

$$210$$ = $$\ \frac{\ 100+x}{100}\left(75+75\right)$$

$$\ 100+x=210\left(\frac{100}{150}\right)$$

x = 40%

The answer is option C.

It is given,

 The number of players who scored more than 60 runs in tournament Q is 75.

 The number of players who scored less than or equal to 20 runs in tournaments Q and R together = 120 + 90 = 210

Required ratio = 75 : 210 = 5 : 14

The answer is option B.

It is given,

Total number of players who scored more than 60 runs in all the three tournaments = 75 + 75 + 60 = 210

The answer is option A.

It is given,

The number of players who scored more than 40 runs in tournament P(L) = 105 

The number of players who scored less than or equal to 40 runs in tournament R(M) = 300 - 90 = 210

M - L = 210 - 105 = 105

The answer is option D.

It is given,

Average number of players who scored more than 20 runs in all the three tournaments = $$\ \frac{\ 240+180+210}{3}=\frac{630}{3}=210$$

The answer is option D.

This question is not clear and is officially removed from CMAT 2023 paper.

1947 = $$1\times3\times649$$ = $$3\times11\times59$$

$$M\times A\times T=1\times3\times649=3\times11\times59$$

Maximum value of M + A + T = 1 + 3 + 649 = 653

The answer is option C.

$$2^6\times3^4\times5^5=\left(2\times5\right)^5\times2\times3^4$$ = $$16200000$$

S($$2^6\times3^4\times5^5$$) = S(16200000) = 9

The answer is option A.

Statement 1 

After drawing 3 masks, there can be 2 combinations possible -All three are of same color or two are of same color and 1 is of different color. Hence we can ensure that we can get two masks of same color after drawing 3 masks, randomly. 

If we draw less than 3 masks i.e. 2 masks , there is a possibility of both the masks being of different color hence we can't ensure that these masks can be of different color, hence the minimum number of masks we need to draw is 3. 

Statement 2 

To calculate the minimum number of students required, we need to consider the worst case scenario i.e. the birthdays of students are evenly spread across all the 12 months. We'll have to assume that there are atleast 5 birthday is each month, so the total number of students required = 5* 12 = 60. To assure that there is 1 month in which we have 6 birthdays, we'll have to add 1 to this number, hence the minimum number of students required = 60 + 1 = 61 

Profits of A and B will be in the ratio of investments, i.e. 4500:2700 = 5:3

Total profit = Rs 256

A's profit = $$\frac{5}{8}\left(256\right)=5\left(32\right)$$ = Rs 160

The answer is option C.