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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. $76$

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Migrated from GO Mechanical 8 months ago by Arjun
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76 satisfying all three condition.
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76 ?
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D is correct
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explain pls

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@Gyanu

+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.
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A question based on logical Implication.

+1 vote

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 (5.1k points)
selected by
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 (7k points)
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
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
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

by Junior (695 points)