Official Quant thread for CAT 2013

Amit started a job alone and Bob joined him after a few days. The work got completed in 8 days.Amit would have required 2 more days to complete the work alone whereas Bob could have completedthe work alone in 25 days. For how many days did Bob work?


(a) 3 (b) 2 (c) 6 (d) 5

Find the value of 'a' in the equation 3x^2 – (3a + 2) x + 7 = 0, if one of its root is 4.

😉 😉

If the natural numbers starting from 1 are written one after the other to form a 121-digit number, then what will be the last digit of the resultant number?

If f(x) = x^2 – 3x + 2 and g(x) = x^3 – 2x, find the value of g(f(x)), for x = 4.

Alok works 25% faster than Bishnoi, who is faster than Charan. Bishnoi takes 10 more days than Arun, to complete a piece of work. Charan works for 11 days and Alok for 19 days. How many days does Bishnoi take to complete the remaining work?

P starts from city A towards city B. After some time, Q and R start from cities A and B respectively at 5 kmph and 12 kmph, towards B and A respectively. The distance between A and B is 100 km. If P and Q meet at 20 km from A, and P and R meet at 28 km from A, what is the speed of P?

mg

In a race on a circular track,there were 12 laps of 150m each.Ram and Shyam were very close till the end of the third lap,but thereafter Shyam went on to win the race by 81 m.If Shyam gained uniformly over Ram in all the remaining laps, the ratio of the speed of Ram and Shyam for each of the other laps was ?

A AND B PICK UP A BALL FROM A RANDOM FROM A BAG CONTINING 5 VIOLET , 2 RED AND 3 ORANGE BALLS ONE AFTER THE OTHER . REPLACING IT EVERY TIME UNTIL 1 GETS THE ORANGE BALL . THE PERSON WHO GETS THE ORANGE BALL IS DECLARED AS THE WINNER . A BEGINS THE GAME , THEN WHAT IS THE PROBABILITY OF B WINNING 👍 THE GAME ?

If PQR=1, the value of the expression 1/1+P+Q^-1 + 1/1+Q+r^-1 + 1/1+R+P^-1 is equal to


a) P+Q+R
b) 1/P+Q+R
c) 1/P + 1/Q + 1/R
d) 1

please look into it, thanks.

what will be the units digit of 413^7753

what will be the last two digits of 84^42?




find the number of ways in which letters of the world INCLUDE can be permuted so that no two vowels appear together??

Two boxes contain 4 and 16 balls respectively. Two balls in the first box and four in the second, are black. If a box is chosen randomly and two balls are drawn at random from it, what is the probability that at least one ball is black?

There are 100 questions in a question paper. Each correct attempt fetches one mark and each wrong attempt attracts a penalty of one-third of a mark. How many different integral scores are possible for a student who attempted exactly 80 questions in the paper?

y = 1/3 + 3/18 + 15/162 +.....
find the value of y^2 + 2y
a) 2
b) 1
c) 15
d) none


correct ans is 2 ..

please explain ???

Given a geometric progression of five terms, each a positive integer less than 100. The sum of the five terms is 211. If S is the sum of those terms in the progression which are squares of integers, then S is:A. 91B. 133C. 195D. 211

100! when expanded, ends in exactly 24 zeroes in decimal system. In how many other number systems, when converted, 100! still ends in exactly 24 zeroes?(For example, 5! = 120 has one zero when expanded in decimal system and it becomes 71 after conversion in base-7 and has no zeroes at end.)A. 21B. 22C. 29D. 30

The largest number amongst the following that will perfectly divide 101^100 - 1 is

100

10,000

100^100

100,000😃

A number N^2 has 15 factors. How many factors can N have? 😍