Number Theory Previous Year Questions (CAT)  Set 0024

Previous years`s CAT questions: Number Theory
Post your solutions as reply to respective questions below.

Question 1
72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?
a. Rs. 3.23
b. Rs. 5.11
c. Rs. 5.51
d. Rs. 7.22 (CAT 1995)

Question 2
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
What was the worth of the total property?
(a) Rs. 30 lakh
(b) Rs. 8 lakh
(c) Rs. 18 lakh
(d) Rs.24 lakhÂ Â (CAT 1994)

Question 3
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
What was Carlâs original share?
(a) Rs. 4 lakh
(b) Rs. 12 lakh
(c) Rs. 6 lakh
(d) Rs. 5 lakhÂ Â (CAT 1994)

Question 4
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
What was the ratio of the property owned by the widows of the three sons, in the end?
(a) 7 : 9 : 13
(b) 8 ; 10 : 15
(c) 5 : 7 : 9
(d) 9 : 12 : 13Â Â (CAT 1994)

Question 5
Mark (a) if I > II.
Mark (b) if I < II.
Mark (c) if I = II.
Mark (d) if nothing can be said.
Last week Martin received $10 in commission for selling 100 copies of a magazine. Last week Miguel sold 100 copies of this magazine. He received his salary of$ 5 per week plus a commission of 2 cents for each of the first 25 copies sold, 3 cents for each of next 25 copies sold and 4 cents for each copy thereafter. ($1 = 100 cents).
I. Martin’s commission in the last week.
II. Miguel’s total income for last week. (CAT 1994)

Question 6
Mark (a) if I > II.
Mark (b) if I < II.
Mark (c) if I = II.
Mark (d) if nothing can be said.
Nineteen year from now Jackson will be 3 times as old as Joseph is now. Johnson is three years younger than Jackson.
I. Johnson’s age now.
II. Joseph’s age now. (CAT 1994)

Question 7
From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?
(a) 2 : 1
(b) 3 : 1
(c) 3 : 2
(d) NoneÂ (CAT 1993)

Question 8
A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to
(a) 20
(b) 5
(c) 30
(d) 35Â Â (CAT 1993)

Question 9
Let x < 0, 0 < y < 1, z > 1. Which of the following may be false?
(a) (x^{2}â z^{2}) has to be positive.
(b) yz can be less than one.
(c) xy can never be zero.
(d) (y^{2}â z^{2}) is always negative.Â (CAT 1993)

Question 10
An outgoing batch of students wants to gift PA system worth Rs.4200 to their school. If the teachers offer to pay 50% more than the students, and an external benefactor gives three times teachers’ contribution, how much should the teachers donate?
(a) 600
(b) 840
(c) 900
(d) 1200 (CAT 1990)