1
June 28, 2020, 12:39 a.m.
If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true?

If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true?
A. n is odd
B. n is prime
C. n is a perfect square

  1. A and C only.
  2. A and B only.
  3. A only.
  4. None of this.
quant
numbers
Add Comment to Question
ANSWERS
2
June 28, 2020, 1:38 a.m.

x is the product of 4 consecutive positive integers, that means its even number (because there will be 2 even numbers and any positive integer multiplied by even gives even)

This makes 'A' is True. i.e. n is odd as even + 1 is odd

for 'B' lets put some values.
it is given that x is product of 4 consecutive positive integers.
Assume consecutive numbers are 1,2,3, and 4 therefore product will be 24.

n = 24 + 1 = 25 (We proved that n is not prime)

For 'C' we cau put values and find or we can use algebra 
(It's easy to find through values)
Using algebra
Let x = y(y + 1)(y + 2)(y + 3)

x = y4 + 6y3 + 11y2 + 6y
Adding and subtracting 1

x = y4 + 6y3 + 11y2 + 6y + 1 - 1
x = (y2 + 3y + 1)2 - 1

n = x + 1
n = (y2 + 3y + 1)2 - 1 + 1
n = (y2 + 3y + 1)2

n is perfect square

Therefore option 1. A and C only

 

Add Comment to Answer
In Order to answer this Question please login
Tags
quant
numbers
cat-2019
varc
rc
set-theory
time-speed-distance
quadratic
geometry
cat
Stats
Total Questions
57
Total Answers
32