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What is trick to solve sillogisms

What will be the remainders when 528^1567 is divided by 13 and 54 respectively?

Two trains are moving in the same direction at the rate of 50 kmph and 80 kmph. The fast train crosses the slower train in 27 seconds. Find length of the faster train.

A and B plays a game. They alternately roll a fair die and the first person to roll a 6 wins the game. If A starts, what is the probability of A wining the game?

In triangle ABC, medians BP and CQ are perpendicular to each other and intersect at R. If BP = 8 and CQ=12, what is the area of triangle ABC? Please give complete solution

In how many ways 1500 be written as a product of three integers? Considering +ve and -ve integers.

in actual cat 2002 question paper, the question(data sufficiency) - "is x=y" how can it be solved? wen i solved, i could also use statement B for solving, whereas in the key they used a diffrent method and i used a different one. the qn and d method i used for statement B is as follows: is x=y? A. (x+y)(1/x + 1/y)=4 B. (x-50)^2 = (y-50)^2 in statement B, y cant we take sq roots on both sides n then say tht x=y??? plz help

dc 16

what should be the minimum correct attempt for 80 in CAT as per the mocks?

If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have?