Quants for CAT2007 - 3

Here goes 5 more questions I know the answer of question number 2, 4 and 5.

Q1. Fermat's Theorem states that the number x = (2p-1 - 1)/p is always an integer if p is an odd prime.
How many values of p exist for which x a perfect square?
a. 0
b. 1
c. 2
d. 3
e. Cant be determined

Q2. What is the next term in the following series?
2, 5/6, 5/12, 15/144

Q3. How many two-digit numbers exist for which the product of its digits is the same as the sum of its digits?
a. 0
b. 1
c. 2
d. More than 2
e. None of the above

Q4. If a radioactive substance has a half-life of 300 years, how long will it take for the substance to decay to 10 of its initial amount?
a. 997 years
b. 995 years
c. 979 years
d. 975 years
e. None of the above

Q5. The probability of a problem being solved by two students is respectively 1/3 and 1/2. The probability that the problem will be solved, is:
a. 2/3
b. 3/4
c. 1/3
d. 1

__________________

n/a

answers

Ans. 1- x is a perfect square only for p = 3

hence, answer is option b.

(since p has to be an odd prime number... however i checked out only till 13)

 

Ans 3 - a 2 = 2a. This is satisfied only for a = 2 and a = 0.

hence option c.

(we can take into consideration a = 0 right?  because i think multiplication with 0 is defined(or it is only division which is ND??). Am not sure about this. can u confirm?)

 

Ans. 5- answer is option a. is tat correct?

lemme know,

Thanks,

Swapna

 Q5's answer is incorrect,

 

Q5's answer is incorrect, rest i am not sure

 

__________________

n/a

why incorrect?

why is it incorrect?

even if one of them solves the problem OR both of them do, then the problem is solved right?

hence: (1/2 * 2/3) + (1/2* 1/3) + (1/2 * 1/3) = 2/3

i.e. either A solves and B doesnt OR B does and A doesnt OR both do it

 

Could you please provide your answer with explanation?

re 2 Q3

post edited

 Sorry for the confusion..

 Sorry for the confusion.. that was all right i was referring to Q3

for which the answer is given as 1 option b

 

__________________

n/a

prob of botth solving is

prob of botth solving is 1/6

hence required prb = 1/2 + 1/3 - 1/6 = 4/6 = 2/3

only possible number i can

only possible number i can think of is 22

ques 4 :  the chemistri

ques 4 : 

the chemistri formula is

Nt = N0 e-kt

trying to find the hallf life by substituting suitable values and taking log.

t1/2  =  ln2 / k 

The above formulae are sufficient to solve the problem.

@ rajorshi

 yaa... me 2 cn think offf only 22...

 

raj yar..approach btna yar....i try 2 solve dis question but nt gettn da rite ansrr( 4 questn no 3)

 

n

 

in ur xplanation 2 probabilty wala questn..isnt it b " + " sign instead of  " - "

appraoch to kuch nahin hai.

appraoch to kuch nahin hai. first look mein 22 fits. baaki ho bhi sakta hai, lekin 1 aadh se jyada nahin hoga.

probability question is simple venn diagram logic

P(A OR B) = P(A) +P(B)-P(AB)

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