Logiqa

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You have twelve identical looking coins, out of which eleven are genuine and weigh the same, and one is a fake, which either weighs less than or more than the genuine coin. Besides this you have a standard two-pan beam balance which allows you to place any number of items in each of the pans.

Find the minimum number of weighings required to guarantee finding the fake coin and determining whether it is heavier or lighter than the genuine coin.

A) 2 weighings
B) 3 weighings
C) 4 weighings
D) 5 weighings
E) Impossible to find the fake coin

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x and y are positive numbers such that
x2 + y2 = 52 and xy = 24.

Assuming x > y, find the value of x2 – y2.

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Which of the above statements are true?

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Each letter represents a single one-digit or two-digit number from 1 to 16 excluding 4 and 9 with no repetition such that the sum of the numbers in each column and row are equal to the integers given on the bottom and the right side of the table.

Find the value of (B + D + F + H + J + K + M) – (A + C + E + G + I + L + N).

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You have invited 8 friends to your birthday party. You have asked the bakery to precut the cake into 9 pieces so that each person, including yourself, gets an equal amount of cake.

A few hours before the party, one of your friends informs you that he is not sure whether he will be able to come.

You call the bakery to change the number of pieces the cake should be precut into.

Find the minimum number of pieces the cake should be precut into, irrespective of the size of each piece, to ensure that each person gets an equal amount of cake irrespective of whether your friend comes or not.

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Alexander and Benjamin start driving to Charles’ house in their respective cars at the same time.

Alexander drives at a constant speed of 4 meters/second whereas Benjamin drives at a constant speed of 5 meters/second.

However, Benjamin’s car is old and overheats on travelling every 200 meters after which Benjamin must stop for 10 seconds before he can continue.

Given that they don’t reach Charles’ house at the same time, who reaches first?

A) Alexander
B) Benjamin
C) Depends on the distance

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The number of 0’s in this box is __.
The number of 1’s in this box is __.
The number of 2’s in this box is __.
The number of 3’s in this box is __.
The number of 4’s in this box is __.
The number of 5’s in this box is __.
The number of 6’s in this box is __.
The number of 7’s in this box is __.
The number of 8’s in this box is __.
The number of 9’s in this box is __.

Fill each blank with a single digit such that each statement in the box holds true.

Submit your answer as the number formed by concatenating the numbers entered in the blanks.

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EVE/DID = .TALKTALKTALK…


In the cryptogram given above each letter represents a distinct digit.

Find the value of EVE + DID + TALK such that the division holds true.

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Alexander, a census taker, wants to know about Amelia’s children. The have the following conversation:

Alexander: How many children do you have?
Amelia: I have three children.
Alexander: What are their ages?
Amelia: I can tell you that the product of their ages is 36.
Alexander: That helps but I still can’t determine their ages.
Amelia: The sum of their ages is the same as today’s date.
Alexander: That narrows it down, but I still can’t determine their ages.
Amelia: What if I told you that my youngest just took her first steps yesterday.
Alexander: That should do it, thank you.

Can you determine the ages of Amelia’s three children?
A) 1, 1, 36
B) 1, 3, 12
C) 1, 4, 9
D) 1, 6, 6
E) 1, 2, 18
F) 2, 2, 9
G) 2, 3, 6
H) 3, 3, 4

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When the positive integer X is divided by 6, the remainder is 2.

What is the remainder when 3X is divided
by 6?

A) 0
B) 1
C) 2
D) 3
E) 4
F) 5

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You visit a special island which is inhabited by two types of people: knights who always speak the truth and knaves who always lie.

Alexander and Benjamin are two inhabitants of the island.

Alexander makes the statement: “We are both liars”

Based on this, what types are Alexander and Benjamin?

A) Alexander is a knight and Benjamin is a knave
B) Alexander is a knave and Benjamin is a knight
C) Alexander and Benjamin are both knights
D) Alexander and Benjamin are both knaves
E)Impossible to determine

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X = (666…666)2 where 100 6s are concatenated
Y = (888…888) where 100 8s are concatenated

Z = X + Y

Find the sum of digits of Z.