The Gateway to Computer Science Excellence
0 votes
180 views

A house has a number which need to be identified. The following three statements are given that can help in identifying the house number?

  1. If the house number is a multiple of $3$, then it is a number from $50$ to $59$.
  2. If the house number is NOT a multiple of $4$, then it is a number from $60$ to $69$.
  3. If the house number is NOT a multiple of $6$, then it is a number from $70$ to $79$.

What is the house number?

  1. $54$
  2. $65$
  3. $66$
  4. $76$
in Numerical Ability by Veteran (422k points)
edited by | 180 views
Migrated from GO Mechanical 5 months ago by Arjun
0
76 satisfying all three condition.
0
76 ?
0
D is correct
0

@shreyansh jain 

explain pls

0

@Gyanu

I have added the answer please check.

+1
For any given house number, all the three statements should be true.

For 76:
1. Since it is not a multiple of 3, it becomes vacuously true.
2. Since it is a multiple of 4, it becomes vacuously true
3. Since it is not a multiple of 6, it becomes vacuously true.

It is vacuously true because $p \implies q$ is true when $p$ is false.
0
A question based on logical Implication.

4 Answers

+1 vote
Best answer

Consider 54:

  • 54 Mod 3 $= 0$ and 54 lies between 50 and 59
  • 54 Mod 4 $\neq 0$ but 54 does not lie between 60 and 69, hence 54 is not the answer

Consider 65:

  • 65 Mod 3 $\neq 0$
  • 65 Mod 4 $\neq 0$ and 65 lies between 60 and 69
  • 65 Mod 6 $\neq 0$ but 65 does not lie between 70 and 79, hence 65 is not the answer

Consider 66:

  • 66 Mod 3 $= 0$ but 66 does not lie between 50 and 59, hence 66 is not the answer

Consider 76:

  • 76 Mod 3 $\neq 0$
  • 76 Mod 4 $= 0$
  • 76 Mod 6 $\neq 0$ and 76 lies between 70 and 79, hence 76 is the answer

D is Correct 😊

by Active (4.9k points)
selected by
+2 votes
It should be 76.

1. 76 is not a multiple of three, so we don't care about the first statement.
2. 76 is a multiple of four, so we don't care about the second statement.
3. 76 is not a multiple of 6 and is present between 70 and 79, hence it is true.

No other option has all the three statements to be true.
by Loyal (6.4k points)
+2 votes
Start by exploring point 2 and 3 as they give more information (NOT cases), although in this particular question it doesn't matter much.

Not a multiple of 4 should be in range 60-69, so 54 is rejected.

Not a multiple of 6 should be in range 70-79, so 65 is rejected.

Multiple of 3 should be in range 50-59, 66 is rejected.

So, House number is 76. Option (D)
by Active (2.2k points)
0
+1 vote
It can be done by back substituting options in answer.
A) 54 ===> is a multiple of 3 so number should be between 50-59
      also 54 is not a multiple of 4 then it should be between 60 to 69
         Here it contradicts so ,this cant be the answer
B) 65==>not a multiple of 3 , so nothing can't be inferred from statement one
     65 is not a multiple of 4 so number is between 60-69
      65 is not multiple of 6 so number is between 70-79
       here is contradiction, so this option is not answer.
C)66===> multiple of 3 hence answer should be between 50-59 , here is contradiction with first statement so this is not answer
D) 76====> not a multiple of 3 , so thing from statement one
76 is multiple of 4 but we dont know what to do when number is multiple of 4
76 is not multiple of 6 so number should be between 70-79 here condition satisfies
so this is the answer

Answer is D
by Junior (655 points)
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,666 questions
56,170 answers
193,842 comments
94,048 users