Independence Day - 77INDIA

# High Level Maths Quiz: Part 7

#### Question 1

Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy , we get the age of the father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger to his father by 3 years.

Then what is the age of the younger boy?
(a) 3
(b) 4
(c) 2
(d) None of these

#### Question 2:

Flights A and B are scheduled from an airport within the next one hour.All the booked passengers of the two flights are waiting in the boarding hall after check in .The hall has a seating capacity of 200 , out of which only 10 % remained vacant.40% of the waiting passengers are ladies. When Boarding announcement came , passengers of flight A left the hall and boarded the flight. Seating capacity of each flight is two third of the passengers who waited in the waiting hall for both the flights put together. Half the passengers who boarded flight A are women.After Boardng for flight A 60% of the waiting hall seats became empty.For every twenty of those who are still waiting in the hall for flight B , there is one airhostess in flight A.

What is the ratio of the empty seat in flight B to the number of Air hostesses in Filght A?
(a) 10:1
(b) 5:1
(c) 20 :1
(d) 1:1

#### Question 3:

Five boys went to a store to buy sweets. One boy had Rs.40 , another boy had Rs.30 .Two other boys had Rs.20 each. The remaining boys boy had Rs.10.Below are some more facts about the initial and final cash position.
(i) A started with more than J
(ii) S spent Rs.1.50 more than D
(iii) G started with more money than just only one other person
(iv) D started with 2/3 of what S started with
(v) A spent the most , but did not end with the least
(vi) J spent the least and ended with more than A or D
(vii) G spent Rs.3.50
(viii) A spent 10times more than what G did.

In the choices given below, all statements except one are false. Which one of the following statements can be true ?
(a) A started with Rs.40 and ended with Rs.9.50
(b) S started with Rs. 30and ended with Rs. 1
(c) G started with Rs. 20 and ended with Rs.4
(d) J started with Rs. 10 and ended with Rs.7

#### Question 4:

Three children won the prizes in the Bournvita quiz contest. They are from the schools : Loyola . Convent and Little flowers which are located in different cities.Below are some of the facts about the schools , the children and the city they areform.
(i) one of the children is Bipin
(ii) Loyola School’s contestant did not come first
(iii) Little Flower’s contestant was named Riaz
(iv) Convent School is not inHyderabad
(v) The contestant from Pune is not from Loyola School
(vi) The contestant from Bangalore did not come first
(vii) Convent School’s contestant’s name is not Balbir.

Which of the following is true?
(a) first prize : Riaz(Little flowers) , 2nd prize : Bipin (Convent), 3rd prize: Balbir (Loyola)
(b) first prize : Bipin (Convent), 2nd prize : Riaz(Little flowers) ,3rd prize: Balbir (Loyola)
(c ) first prize : Riaz(Little flowers) ,2nd prize : Balbir (Loyola), 3rd prize : Bipin (Convent)
(d) first prize : Bipin (Convent), 2nd prize : Balbir (Loyola), 3rd prize: Riaz(Little flowers)

## Answers with Solution

#### 1)( c) is the right answer.

Only two combinations are possible
Younger  Older
2              4
3               9

Cubes of natural number are 1, 8, 27, 64 ….. Here, 64 and above is not possible as the age will go above 10. only (b ) and (c ) satisfies the case of mother and father.

#### 2) (a) is the correct answer

→ Total seats in the hall = 200
→ Seats vacant =20
→ Total waiting =180
→ Ladies = 72
→ Seating capacity of flight = 2/3 *180 =120
→ Number of people in Flight A = 100 for Flight B = 180 – 100 = 80
→ Thus ,number of air hostess for A= 4
→ Empty seats in the flight B = 120-80 = 40
→ 40 : 4 = 10:1

#### 3) (D) is the correct answer

→ Option (c ) is ruled out by statement (vii)
→ Option (a)is ruled by statement (vii) and (viii)
→ From statement (iv) , S had Rs. 30 to start and D Rs. 20
→ From statement (ii), option B is not possible as S was left with Rs. 1 , he spent Rs. 29 but according to the (b) he spent Rs. 1.50 more than D.But D had only Rs. 20 Hence option (D) is correct.

#### 4) (c) is the correct answer

Statements (v) and (vi) rule out the option (a) and (b). The contestants from Bangalore and Pune did not come first so, school from Hyderabad can come first. Convent is not in Hyderabad which rules out option (d)