Number System - Questions & Discussions

MBA CAT 2022
2816
Thanks guys...
This is another problem:

Q) A number N when divided by a divisor D gives a remainder of 52. The number 5N when divided by D gives a remainder of 4. How many values of D are possible?
A.1
B.3
C.6
D.7

N=k.D + 52

5N= 5k.D + 260

Above when divided by D, remainder will be 260 mod D = 4

=> D can be 256 or any factor of 256 >52

viz. 256,128,64

so answer should be 3
2817
Thanks guys...
This is another problem:

Q) A number N when divided by a divisor D gives a remainder of 52. The number 5N when divided by D
gives a remainder of 4. How many values of D are possible?
A.1
B.3
C.6
D.7


In first case "N" it is giving remainder of 52 so "5N" should ideally give remainder of 52*5 = 260, but it is giving remainder of 4, it means 256 is multiple of D and also it should be greater than 52. So, 64, 128 and 256 can be the values of D.

So, answer is B i.e., 3
2818

I am facing problem in these questions:

Q1. The sum of 20 numbers (may or may not be distinct) is 801. What is their minimum LCM possible?
A.36
B.42
C.56
D.60

Q2. The sum of 20 distinct numbers is 801. What is their minimum LCM possible?
A.480
B.360
C.840
D.420

Q3. What is the smallest positive composite number generated by the expression p2 - p - 1 where p is a
prime number?
A.13
B.155
C.40
D.270

2819

The Answer is only II

2820

When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be
purchased for the original price. How many oranges can be purchased for 24 dollars at the original
price?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24

2821
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be
purchased for the original price. How many oranges can be purchased for 24 dollars at the original
price?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


let the price of one orange is x so for 12 rupees he can buy 12/x oranges and as the price becomes 0.6x no he can purchase 20/x oranges
20/x-12/x=4
x=2
for 24 dollars he can purchase 12 oranges
whats the oa?
2822

Thanks...that is right!!!!

Another question:

A piece of string 35 inches long is cut into three smaller pieces along the length of the string. The
length of the longest piece is three times the length of the shortest piece. Which one of the following
could equal the length of the medium-size piece?
(A) 5
(B) 7
(C) 10
(D) 16
(E) 20

My approach:

x>y>z
x=3z
4z+y = 35

Not able to get an answer by solvin this...

2823
Thanks...that is right!!!!

Another question:

A piece of string 35 inches long is cut into three smaller pieces along the length of the string. The
length of the longest piece is three times the length of the shortest piece. Which one of the following
could equal the length of the medium-size piece?
(A) 5
(B) 7
(C) 10
(D) 16
(E) 20

My approach:

x>y>z
x=3z
4z+y = 35

Not able to get an answer by solvin this...

4z+y=35
y=10 z=6.25 x=18.75
ie c)
if y=16 z=4.75 x=14.75
but x>z so c satisfies
2824
I am facing problem in these questions:

Q1. The sum of 20 numbers (may or may not be distinct) is 801. What is their minimum LCM possible?
A.36
B.42
C.56
D.60

Q3. What is the smallest positive composite number generated by the expression p2 p 1 where p is a
prime number?
A.13
B.155
C.40
D.270


1) My take is 42.

801 = 42*19 + 3.
LCM(42,3) = 42.

3) My take is 155.

Use the property that primes are of the form 6k+1 or 6k-1.
2825
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be
purchased for the original price. How many oranges can be purchased for 24 dollars at the original
price?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


My take is 12.

12/x - 12/0.6x = 4.
=> x = 2.
Hence 24/2 = 12 oranges can be purchased in original price.
2826

Hi Al

I am stuck up with these two problems.. pls help me out

2827

Option II Only

2828
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be
purchased for the original price. How many oranges can be purchased for 24 dollars at the original
price?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


option B :12
let price of 1 orange be x.
price after reduction - 0.6x
using first statement - 12/x number of oranges can be bought = say y.
using second statement - 12/06.x = y +4 number of oranges can be bought.
using the two equations and solving,x = 2;
so using 24$ and cost of one orange being 2$, 12 oranges can be bought.
2829

How many numbers from 7, 13, 14, 21, 26, 39 and 91 divide (69^12 38^12)?
OPTIONS

1)7
2)5
3)3
4)1
5)None

2830
How many numbers from 7, 13, 14, 21, 26, 39 and 91 divide (69^12 38^12)?
OPTIONS

1)7
2)5
3)3
4)1
5)None


My take is 3.

It is divisible by 7,13 and 91.
Used Euler's.
2831

I have a question:


Q)
The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of
the number of employees who are graduate and above, to that of employees who are not, can
possibly be (CAT 2006)
A.97: 84
B.87: 100
C.85: 98
D.101: 88
E.110: 111


I found out the solution as D.
Please give inputs.

2832
I am facing problem in these questions:

Q1. The sum of 20 numbers (may or may not be distinct) is 801. What is their minimum LCM possible?
A.36
B.42
C.56
D.60

Q2. The sum of 20 distinct numbers is 801. What is their minimum LCM possible?
A.480
B.360
C.840
D.420

Q3. What is the smallest positive composite number generated by the expression p2 p 1 where p is a
prime number?
A.13
B.155
C.40
D.270




Answers are given as
Q1: A
Q2: B
Q3: B
2833
I have a question:


Q)
The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of
the number of employees who are graduate and above, to that of employees who are not, can
possibly be (CAT 2006)
A.97: 84
B.87: 100
C.85: 98
D.101: 88
E.110: 111


I found out the solution as D.
Please give inputs.


A.97:84 (97+84=181 is a prime no.)
B.87:100(87+100=187 is divisible by 11. So, not a prime no.)
C.85:98(85+98=183 is divisible by 3. So, not a prime no.)
D.101:88(101+88=189 is divisible by both 3 and 9. So, not a prime no.)
E.110:111(110+111=221 is divisible by 13. So, not a prime no.)

So, the answer should be A.97:84
2834
My take is 3.

It is divisible by 7,13 and 91.
Used Euler's.


Can you please explain.
2835
How many numbers from 7, 13, 14, 21, 26, 39 and 91 divide (69^12 38^12)?
OPTIONS



1) 7
2) 5
3) 3
4) 1
5) None