All India CAT Group

In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?
  • a)
    5
  • b)
    8
  • c)
    1
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Pranav Khalate answered  •  yesterday
⇒ Let the 1st, 2nd, 3rd and 4th digits be a,b,c and d respectively.
So, four-digit no. will be dcba

→ According to the given question,
⇒ a+b=c+d --- ( 1 )
⇒ a+d=c --- ( 2 )
⇒ b+d=2(a+c) ---- ( 3 )

∴ a+b=a+2d [ Substituting value of equation ( 2 ) in equation ( 1 ) ]
∴ b=2d --- ( 4 )

⇒ 2d+d=2(a+a+d
... more
Shanti Devi asked a question

Directions: Read the following information carefully and answer the question that follows.
In a village of Bastar district in Madhya Pradesh, only two types of people live who belong to a tribal class. The first type is known as class A, while the other is known as class B. In that village, there is no other type of person except these two. The activities of both types of people are governed by perfectly patterned norms of social behaviour. Each person of the tribe has to obey the norms. They are rigid about this.
As far as marriage is concerned, the following norms are to be followed:
(A) The people of class A cannot marry any other member of their own class, though they can marry members of class B.
(B) After being married, each male member ceases to be member of that class in which he was born, but automatically he becomes the member of the other class to which his wife belongs.
(C) As far as females are concerned, they remain the members of their own class after being married.
(D) On its birth, the child automatically becomes the member of its mother's class.
(E) When any male member becomes widower or divorcee, then he again belongs to the group in which he was born.
(F) Nobody can marry more than one person according to social laws.
Any female of class B can have
(P) grandfather (father's father) born in class B
(Q) grandmother (father's mother) born in class B
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Asha Rohiya asked a question

Directions: Read the following information carefully and answer the question that follows.
In a village of Bastar district in Madhya Pradesh, only two types of people live who belong to a tribal class. The first type is known as class A, while the other is known as class B. In that village, there is no other type of person except these two. The activities of both types of people are governed by perfectly patterned norms of social behaviour. Each person of the tribe has to obey the norms. They are rigid about this.
As far as marriage is concerned, the following norms are to be followed:
(A) The people of class A cannot marry any other member of their own class, though they can marry members of class B.
(B) After being married, each male member ceases to be member of that class in which he was born, but automatically he becomes the member of the other class to which his wife belongs.
(C) As far as females are concerned, they remain the members of their own class after being married.
(D) On its birth, the child automatically becomes the member of its mother's class.
(E) When any male member becomes widower or divorcee, then he again belongs to the group in which he was born.
(F) Nobody can marry more than one person according to social laws.
Q. A boy who was born in class B (boy and his wife both can have married and unmarried brothers) can have
... more

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