# Question Bank (Quant) - Nilanjan Dutta, CAT 2016 - 100 Percentiler

• Number of Questions - 30
Topic - Quant Mixed Bag
Source - CAT Preparation by Unacademy

• Q1) Let N = 486486486486….up to 484 digits. What is the remainder when N is divided by 375?

a) 364
b) 239
c) 182
d) 114

• Q2) Three persons, A, B and C, have a certain number of chocolates with each of them. The number of chocolates with B is 20% more than that with A, which, in turn, is two-thirds of that with C. If the number of chocolates with B is less than the total number of chocolates with A and C together by x percent, what is the value of x?

a) 30
b) 40
c) 48
d) 52

• Q3) A function is defined as F(N) = F(N - 1) + F(N - 2). If F(16) = 987 and F(20) = 6567, find F(18)

a) 3571
b) 1597
c) 4181
d) 2584

• Q4) Which of the following cannot be the sum of the squares of 12 consecutive natural numbers?

a) 8570
b) 5640
c) 6770
d) 9890

• Q5) All numbers from 1 to 300 (in decimal system) are written in base 8 and base 11 systems. How many of the numbers will have a non-zero unit digit in both base 8 and base 11 notations?

a) 239
b) 241
c) 242
d) 236

• Q6) One can go from city A to city C either directly or via city B. If one can go from A to C in a total of 32 ways, from A to B in eight ways and from A to C directly in eight ways, then in how many ways can one go from B to C?

a) 2
b) 3
c) 4
d) 6

• Q7) If log 3, log ( 3^x - 2), log (3^x + 4) are in AP. What will be the value of x?

• Q8) A function is defined from a set X ≡ {C, A, T} to set Y ≡ {B, L, A, C, K, I}. What is the probability that it is a one-one function?
A) 40/243
B) 216/729
C) 5/9
D) None of These

• Q9) 64 men working 8 hour a day plan to complete a piece of work in 9 days . However , 5 days later they found that they had completed only 40% of the work. They now wanted to finish the remaining portion of the work in 4 more days. How many hours per day should they need to work in order to achieve the target ?
a) 11
b) 12
c) 13
d) 15

• Q10) Using the digits 0, 1, 4, 5, 6, 9, how many numbers can be formed such that the last two digits (ten’s and unit’s place) form a perfect square? All the digits need not be used but there should not be any repetition of digits.
a) 252
b) 288
c) 360
d) 336
e) 396

• Q11) A train A starts from town A for town B at 6 am. Another train B leaves town C, which is 600km from town A in the direction of town B, at 7 am. The two trains meet each other at 11 am at a place which is exactly between towns A and C. thereafter they continue to their destination. If train A reaches B 3.5 hours after train B reaches A, find the distance between the towns A and B?

(A) 750 km
(B) 720 km
(C) 675 km
(D) 650 km

• The trains meet at 11 am at the place which is 300km from A & C.
Speed of train A = 300/5 = 60 km/h
Since train B covers the distance upto the midpoint in 4 hours, it will reach town A 4 hours after they meet.
Hence train A will reach town B 7.5 hours after they meet.
Total time taken by train A to reach town B = 5+7.5 = 12.5 hours
Hence distance between A and B = 750 km.

• Q12) 50 students are surveyed about their possession of smartphones, tablets and laptops. Of them, 22 own smartphones, 15 own tablets and 14 own laptops. Nine of these students own exactly two of these items and one student owns all three. How many of the 50 students own none of the three items?
(A) 8
(B) 9
(C) 10
(D) 11

• @Sri-Kanth Correct!
Short trick : 375=125 * 3 and N mod 3 = 1. Only 1st option satisfy
Method full : N mod 125 = 864/125 (last three digits of N mod 125) = 114
N mod 3 = 1
SO N = 125k + 114
N = 3p + 1
125k + 113/3 = p
K= 2 p=121
So rem = 121 * 3 + 1 = 364
[Credits : Abhishek Smarty]

• @Sri-Kanth Correct.
Let A have 100 chocolates and B have 20% more, ie 120 chocolates.
A has 2/3 rd chocolate of C. So C = 120 * 3/2 = 150 chocolates.
B has 130 less from A + C together.
So percentage will be (130/250) * 100 = 52%
[Credits : Gyan Jyoti Sahoo]

• @Sri-Kanth Correct.
40% work is completed in 40 hours (as 64 people are working in all the days, ignore 64 from calculations)
Remaining work = 60%
Required work hours = 60
Remaining Days = 4
So required work hours/day = 60/4 = 15

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