[Download PDF] MAT 2004 Question Paper Paper with Solutions

Instructions

For the following questions answer them individually

Question 151

If Dennis is $$\frac{1}{3^{rd}}$$ the age of his father Keith now, and was $$\frac{1}{4^{th}}$$ the age of his father 5 years ago, then how old will his father Keith be 5 years from now?

Video Solution

Solution

Let Keith's present age be $$3x$$ years and Dennis's present age be $$x$$ years

=> According to ques,

=> $$(3x-5)=4\times(x-5)$$

=> $$3x-5=4x-20$$

=> $$x=15$$

$$\therefore$$ Keith's age after 5 years = $$3(15)+5=50$$ years

=> Ans - (D)

Question 152

A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?

Video Solution

Question 153

The ages of the two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages, in years, are

Video Solution

Solution

Let present ages of the two persons be $$x$$ and $$(x-20)$$ years

According to ques,

=> $$(x-5)=5\times(x-20-5)$$

=> $$x-5=5x-125$$

=> $$4x=120$$

=> $$x=\frac{120}{4}=30$$

$$\therefore$$ Their present ages = 30, 10 years

=> Ans - (B)

Question 154

A person has deposited Rs. 13,200 in a bank which pays 14% interest. He withdraws the money and invests in Rs. 100 stock at Rs. 110 which pays a dividend of 15%. How much does he gain or lose?

Video Solution

Solution

Principal sum = Rs. 13,200 and rate of interest = 14%

=> Interest earned = $$\frac{14}{100}\times13200=Rs.$$ $$1848$$

Thus, number of shares purchased = $$\frac{13200}{110}=120$$

=> Income from stock = (15% of Rs. 100) x 120

= $$15\times120=Rs.$$ $$1800$$

$$\therefore$$ Loss = $$1848-1800=Rs.$$ $$48$$

=> Ans - (A)

Question 155

If a% of x is equal to b% of y, then c% of y is what % of x?

Video Solution

Solution

Given : a% of x is equal to b% of y

=> $$ax=by$$

=> $$y=\frac{ax}{b}$$

Multiplying both sides with $$(\frac{c}{100})$$

=> $$\frac{c}{100}\times y=(\frac{c}{100})\times(\frac{ax}{b})$$

=> $$c\%$$ of $$y=\frac{x}{100}\times\frac{ac}{b}$$

$$\therefore$$ $$c\%$$ of $$y$$ is $$(\frac{ac}{b})\%$$ of $$x$$

=> Ans - (B)

Question 156

The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of the girls is

Video Solution

Solution

Let total strength of class = 100

Let number of boys be $$x$$ and number of girls be $$(100-x)$$

According to ques,

=> $$x-(100-x)=\frac{12}{100}\times100$$

=> $$2x-100=12$$

=> $$x=\frac{112}{2}=56$$

Thus, boys = 56 and girls = 44

$$\therefore$$ Required ratio = $$\frac{56}{44}=14:11$$

=> Ans - (B)

Question 157

Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

Video Solution

Solution

A triangle can be formed by taking any two points of a straight line and third point on the second straight line

=> Number of ways = $$(C_2^{10}\times11)+(C_2^{11}\times10)$$

= $$495+550=1045$$

=> Ans - (C)

Question 158

The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions?

Video Solution

Solution

Let numbers be $$22x$$ and $$22y$$, where $$x$$ and $$y$$ are co-prime numbers.

=> $$22x+22y=462$$

=> $$(x+y)=\frac{462}{22}=21$$

Now, number of possible values of $$(x,y)=(1,20) (2,19) (4,17) (5,16) (8,13) (10,11)$$

$$\therefore$$ There are 6 such pairs.

=> Ans - (D)

Question 159

In a class, 40% of the boys is same as 1/2 of the girls and there are 20 girls. Total number of students in the class is

Video Solution

Solution

Number of girls = 20

Now, 40% of boys = 10

=> $$100\%$$ boys $$\equiv10\times\frac{100}{40}=25$$

$$\therefore$$ Total students = $$20+25=45$$

=> Ans - (B)

Question 160

A man bets on number 16 on a roulette wheel 14 times and loses each time. On the $$15^{th}$$ spin, he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and is therefore unable to decide whether to bet on 16 or 12 in the $$15^{th}$$ spin. Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36).

Video Solution

CAT Content

MAT 2004 Question Paper

If Dennis is $$\frac{1}{3^{rd}}$$ the age of his father Keith now, and was $$\frac{1}{4^{th}}$$ the age of his father 5 years ago, then how old will his father Keith be 5 years from now?

The ages of the two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages, in years, are

A person has deposited Rs. 13,200 in a bank which pays 14% interest. He withdraws the money and invests in Rs. 100 stock at Rs. 110 which pays a dividend of 15%. How much does he gain or lose?

If a% of x is equal to b% of y, then c% of y is what % of x?

The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of the girls is

Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions?

In a class, 40% of the boys is same as 1/2 of the girls and there are 20 girls. Total number of students in the class is

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