Dear All,

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

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Dear All,

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

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

- sadmin
- Site Admin
**Posts:**212**Joined:**Wed Feb 13, 2013 5:51 am

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.

(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
**Posts:**9**Joined:**Thu Feb 28, 2013 7:13 am

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

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

- sadmin
- Site Admin
**Posts:**212**Joined:**Wed Feb 13, 2013 5:51 am

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

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

- sadmin
- Site Admin
**Posts:**212**Joined:**Wed Feb 13, 2013 5:51 am

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

- sadmin
- Site Admin
**Posts:**212**Joined:**Wed Feb 13, 2013 5:51 am

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