 ## Doubts of Number Theory Sheet -3

In this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.

### Doubts of Number Theory Sheet -3

Dear All,

Pleas post your doubts of number theory sheet 3 on this thread.

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### Re: Doubts of Number Theory Sheet -3

Doubt 1- Question number 17 and 18 (PRACTICE QUESTIONS)
(Kindly explain the logic)

Doubt 2- Question number 14 (DATA SUFFICIENCY)
(I am getting cyclicity as 12 for the (15^(x-1)/13) thing that implies that X must be a factor of 13, kindly correct if i am wrong, or point if some error is present in the question)

Doubt 3- Question number 28, the 2431(11*13*17); the fourth number can be 19 or 23, as there s no other constraint, only condition is ascending order. Kindly correct me if I am wrong.
Seema Devi

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### Re: Doubts of Number Theory Sheet -3

Number Theory Sheet 3/Q17
Chandraprakash © meets his friend Raviprakash ®
after a span of 20 years. C asks R about the number of
children that he has and their ages. Hearing this R
replies “I have 3 boys and the product of their ages is
72. Also the sum of their ages is the same as the last
two digits of the pincode of this area”. C examines the
last two digits of the pincode and tells R that the problem
is indeterminate. Then R tells him that his eldest son
had just won a gold medal at the 100 m race which was
held in the school. What is the age of the eldest son of
R
(a) 18 (b) 36
© 24 (d) None of these

Solution

As the product of the three childrens' ages is 72 therefore factorizing 72 into a product of three factors should give us the product 72

72 = 1 X 3 X 24,1X2X36,1X4X18,1X6X12,1X8X9,2X3X12,2X4X9,2X6X6,3X4X6,3X8X3

The clue to understanding this question is that out of all the possibilities, the sum of the ages of the three sons is a two digit number. But if C's friend R could not answer this question after looking at the last two digits of the pin code - the only reason must have been that there are more than two possibilities for that two digit number.

This happens only in the case of 3x3x8 and 2x6x6 - In both these cases the sum is 14. Now when C says he has an eldest son - he clearly indicates that he has one son who is the eldest of the three brothers - Thus the possibility that fits the conditions here is 3x3x8.

Ans to Q17 - is D and Q18 is a

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### Re: Doubts of Number Theory Sheet -3

Fermat's Little theorem states that if

HCF (a,b) = 1

THEN a^(b-1) gives a remainder of 1 on being divided by b

Hope this helps you in understanding the answer in the data sufficiency Q 14

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Joined: Wed Feb 13, 2013 5:51 am

### Re: Doubts of Number Theory Sheet -3

You are correct- tHE QUESTION Must be corrected as "There are four consecutive prime numbers in ascending order" 