Number Systems, Progressions

how many factors of 10^100 are not an integral power of 10^10?

  • none of these.
  • 10190
  • 10191
  • 10081
  • 10080

0 voters

This looks like one of the most important chapters for CAT and the books also lists so but the scenario isn't the same in examinations. You spend a lot on number systems but if you look into the

number of questions asked to the time spent ratio, you'll be astonished by the results !!
So I advice to divide the time judiciously.
-from experience.

Is the sum of 'n' terms of an arithmetic progression divisible by K?

1) The first term and the n th term of the progression are divisible by K.

Please reply if we can determine the question asked by knowing just the option 1.
  • Yes
  • No

0 voters

A simple but tricky problem:
Fresh grapes contain 80% water, dry grapes contain 10% water. What is the weight of dry grapes that can be obtained from 40 kg of fresh grapes ?

  • 10
  • 11
  • 8
  • 9

0 voters

[50^51^52] / 11 -- What is the remainder ? Can some one also post the approach without using the 'mod' method.


S = {n1, n2, n3, n4 .....n2004}; where n1, n2, n3, .... are consecutive primes starting from the first odd prime. P = n1 × n2 × n3 × n4 × ...... n2004. P is a 'm'-digit number. The units digit of the remainder when P is divided by 10m–1 is:

sorry guys.. i dont know the answers.. somebody explain!!

  • 0
  • 7
  • 5
  • 3

0 voters

Remainder when 128^1000 is divided by 153 is:

  • 52
  • 103
  • 145
  • 118

0 voters

If b>a, then which is greater (a)^b or (b)^a ? How to solve this.

help me out in this guys..

What is the least value of x such that 60!/x will be an odd no.?

I don't know d ans and no options.

How many multiples of x exists from a to b(both inculsive) when

i)neither a nor b is a multiple of x

ii)one of a and b is a multiple of x

iii)both a and b are multiple of x

wat will b the initial step for this ?


A number when divided by 5 and 7 successively leaves the the remainders 2 and 4 resptively. What is the remainder when the same number is divided by 35 ?

A 5-digit no is formed from 1,3,5,7 and 9 without repeatition. What is the sum of all such possible numbers?

Can anyone explain..

@Anonymous

Twinkle tellsRaveena that she has got 3 kids and 2 of these kids are twins, andalso that their ages are all integers. She tells Raveena the sum of theages of her kids and also the product of their ages. Raveena says thatshe has insuficient information to determine the ages, but onepossibility is that the twins are a prime number of years old. IfTwinkle's twins are teenagers and their age is not prime, then the sumof the ages of her kids is



37 answers 1) A prime number



35 answers 2) Is greater than 43



87 answers 3) A composite number



53 answers 4) Exactly 2 of the foregoing



228 answers 5) Still undeterminable



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Answer Plz

Integer 39276 & 38304 leaves same remainder when divided by 3 digit natural number n . How many possible value n can have

Hi Pguys, i have few questions, please provide proper solutions and the method in a simplified way (please!!) because all i want is to know the concept better. Thanks in advance. 👏

q1. which of the following represents largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21 , 33 and 54.
a) 9123 b) 9383 c) 8727 d) none

q2. A long part of wood of same length when cut into equal pieces each of 242 cms, leaves a small piece of length 98 cms. If this part were cut into equal pieces each of 22 cms, the length of leftover wood (in cms) would be
a) 76 b) 12 c) 11 d) 10

q3. Define a number K such that sum of squares of first M natural numbers where Ma) 10 b) 11 c)12 d) none

q4. if you form a subset of integers chosen from between 1 to 3000, such that no two integers add upto a multiple of 9, what can be max. numbers of elements in the subset(include 1 and 3000)
a) 1668 b) 1332 c) 1333 d) 1336

q5. What is the highest power of 3 available in the expression 58!-38!?
a) 17 b) 18 c) 19 d) none

q6. How many integer values of x and y are there such that 4x+7y=3, while |x|a) 144 b) 141 c) 143 d) 142

q7. A has a certain nos of toffees, such that if he distributes them amongst 10 children he has 9 left, if he distributes amongst 9 children he would have 8 left, if he distributes amongst 8 childrens he would have 7 left.. and so on until if he distributes amongst 5 children he should have 4 left. What is the second lowest number of toffees he could have with him?
a) 2519 b) 7559 c) 8249 d) 5039

q8. how many identical terms in two AP's 1,3,5.. upto 120 terms and 3,6,9,.. upto 80 terms? i just want to know how to find the last common term between the series??

hello everyone...can someone tell me good books for quant?



Find the largest power of 2 that divides [2²º¹³/(2²º + 13)] completely where [x] is the greatest integer less than or equal to x.

A. 0

B. 7

C. 13

D. 20