# IPMAT Question Paper 2019 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 14

IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: IPM Sample Paper

Question 14 : Let the set = {2,3,4,..., 25}. For each k ∈ P, define Q(k)= {x ∈ P such that x > k and k divides x}. Then the number of elements in the set $P - U_{k=2}^{25} $\$ Q$k) is

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

Let’s take a close look at the definition of Q(k).

Q (k) = {x ∈ P such that x > k and k divides x}.
That means Q(k) contains all the multiples of k in P which are greater than k.

$U_{k=2}^{25} $\$ Q$k) means Q(2) U Q(3) U Q(4) U ………… U Q(25).

Therefore, Q(2) U Q(3) U Q(4) U ………… U Q(25) will include every composite number in P.

Because every composite number is a multiple of at least one prime number lesser than itself.

For Example, 21: Q(3) contains 21, Q(7) contains 21.
So, 21 is surely present once in Q(2) U Q(3) U Q(4) U ………… U Q(25) ( once and only once, because repetitions are neglected in Union)

But Q(2) U Q(3) U Q(4) U ………… U Q(25) will not include prime numbers in P at all.

Because, a prime number can never be expressed as a multiple of another number except 1, which is not present in P.

So we can conclude that Q(2) U Q(3) U Q(4) U ………… U Q(25) contains only composite numbers.
That is, $U_{k=2}^{25} $\$ Q$k) contains only composite numbers.

Therefore, $P - U_{k=2}^{25} $\$ Q$k) = P – {composite numbers in P} = {prime numbers in P} ={2,3,5,7,11,13,17,19,23}

So, the number of elements in the set $P - U_{k=2}^{25} $\$ Q$k) = the number of elements in the set {2,3,5,7,11,13,17,19,23} = 9.

The number of elements in the set $P - U_{k=2}^{25} $\$ Q$k) is 9.

The question is "Let the set = {2,3,4,..., 25}. For each k ∈ P, define Q(k)= {x ∈ P such that x > k and k divides x}. Then the number of elements in the set $P - U_{k=2}^{25} $\$ Q$k) is"

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com