CAT 1997 Question Paper

Expression can be reduced to 16n + 7 + $$\frac{6}{n}$$
Now to make above value  an integer n can be 1,2,3,6,-1,-2,-3,-6
Hence answer will be D).

Let's say he buy fruits of weights 3 kg., 4kg., 5 kg.
Total kilograms of dry fruits $$=3+4+5=12$$

Overall cost price $$=3\cdot100+4\cdot80+5\cdot60=300+320+300=920$$

So cost price per kg. $$=\dfrac{300+320+300}{12} = \dfrac{920}{12}$$

Selling price = $$\dfrac{920}{12} \times \dfrac{3}{2}$$ = 115 per kg (Since Profit is 50%)

Hence answer will be D.

Let the total weight of fresh grapes be 100 gm.

=> Fresh grapes have 90 gm of water and 10 gm of fruit.

When these grapes are dried, the amount of fruit does not change.

=> 10 grams will become 80% of the content in dry grapes

=> Weight of dry grapes = $$\frac{10}{0.8}$$ = 12.5 gm

So, the weight of fresh grapes reduces to 1/8th of its original weight.

=> 20 kg of fresh grapes give 2.5 kg of dry grapes.

Let's say length of express train = $$x$$
So length of goods train = $$2x$$
Total length travelled by express train = $$3x = ((80-40) \times \frac{5}{18}) \times 54 $$ (Where $$(80-40) \times \frac{5}{18})$$ = relative velocity of express train w.r.t. goods train in meter/sec.)
So $$x =200$$ meter.
Now crossing a plateform of length 400 m., total length travelled by train = 600 m=$$t\times(80 \times \frac{5}{18})$$
$$t = 27$$ sec.

let's say number is x.

So $$\frac{7x}{8} - \frac{7x}{18} = 770$$

or $$x = 1584$$

When PQ = 64

Possible values of P and Q are as follows:

64 and 1 ; 32 and 2 ; 16 and 4 ; 8 and 8

So possible sums are 65,34,20 and 16

Hence answer would be D)

Total marks = 80 x 10 = 800
Total marks except highest and lowest marks = 81 x 8 = 648
So Summation of highest marks and lowest marks will be = 800 - 648 = 152
When highest marks is 92, lowest marks will be = 152-92 = 60

$$x_1 + x_2 = 2$$
and $$7x_2 - 4x_1 = 47$$
So $$x_1 = -3$$ and $$x_2 = 5$$ 
And $$c = x_1 \times x_2 = -15$$

Given:
$$\pi((r_1)^2 + (r_2)^2) = 153\pi$$
So 
$$(r_1)^2 + (r_2)^2 = 153$$
Or $$((r_1) + (r_2))^2 - 2(r_1)(r_2) = 153$$
Or  $$(r_1)(r_2) = 36$$ and $$(r_1) + (r_2) = 15$$
$$r_1 = 12$$
$$r_2 = 3$$
Ratio = 4

Let's say m=5k and n=5t
So m-n = 5(k-t) will be divisible by 5.
$$m^2 - n^2 = 25(k^2 - t^2)$$ will be divisible by 5.
$$m+n = 5(k+t)$$ will be divisible by 5 but not necessarily with 10.