## Aptitude Test Shortcuts

**Choosing People to form Groups **

** **Q 2 .Find the no. of ways in which 6 people can be divided into

(i) two groups consisting of 4 & 2 people,

(ii) two groups consisting of 3 people each.

(iii) group 1 and group 2, with 3 people in each group.

SOLUTION

of ways = 6C4

2C2 = 15

of ways =6C3

3C3 2! = 10

**Note: **Divide by 2! since the 2 groups are of equal size.

of ways = 6C3

3C3 = 20

**Note: **Don’t divide by 2! since the 2 groups are labeled.

**Choosing Letters, Balls or other Identical Objects**

** **Q 3 . Seven cards each bear a single letter, which together spells the word “MINIMUM”. Three cards areto be selected. The order of selection is disregarded. Find the number of different selections

**SOLUTION**

Case 1: No. of ways of choosing 3 identical letters = no. of ways of choosing “MMM” = 1

Case 2: No. of ways of choosing “MM” + 1 other letter = no. of ways of choosing I, N, U = 3C1 = 3

Case 3: No. of ways of choosing “I I” + 1 other letter = no. of ways of choosing M, N, U = 3C1 = 3

Case 4: No. of ways of choosing 3 different letters = no. of ways of choosing M, I, N, U = 4C3 = 4

total no. of selections = 1 + 3 + 3 + 4 = 11

**Arranging People**

Q 4. Anne and Bob and 2 other people are to sit in a row. How many ways can this be done if

(i) there are no restrictions?

(ii) Anne must sit on the left and Bob on the right?

(iii) Anne and Bob must sit together?

(iv) Anne and Bob must be separate?

**SOLUTION**

(i) No. of ways of arranging 4 people = 4! = 24

(ii) No. of ways of arranging the other 2 people = 2! = 2

(iii) Treat Anne and Bob as 1 item.

No. of ways of arranging 3 items no. of ways of arranging Anne & Bob = 3! 2! = 12

(iv) No. of ways = 24 – 12 = 12

** ****Arranging Different Types of People (e.g. Boys & Girls)**

Q 5 . In how many ways can 3 boys & 3 girls be arranged in a row if

(i) there are no restrictions?

(ii) the 1st person on the left is a boy?

(iii) the person on each end is a boy?

(iv) the boys are together?

**SOLUTION**

(i) No. of ways of arranging 6 people = 6! = 720

(ii) No. of arrangements = 3C1 no. of ways of arranging the other 5 people = 3C1 5! = 360

(iii) No. of arrangements = 3C2 2! no. of ways of arranging the other 4 people= 3C2 2! 4! = 144

(iv) Treat the 3 boys as 1 item.

No. of ways of arranging 4 items = 4!

The boys can be arranged among themselves in 3! ways

no. of arrangements = 4! 3! = 144

Q 1. A MAN HAVE SOME APPLES HE SOLD 30% OF IT BUT HE STILL REMAIN 420 APPLES. FIND OUT TOTAL NUMBER OF APPLES HE HAVE ?

**SOLUTION**

= (420/70)* 100 =600 APPLES

Q 2. THE AGE OF RAM IS 10% MORE THAN THE AGE OF FARHAN . FIND OUT BY HOW MUCH % FARHAN AGE IS LESS THAN BY RAM ?

**SOLUTION**

= (10/110 )* 100= 9.09 %

Q 3.THE INCOME OF B IS 40% LESS THAN THE INCOME OF A.

FIND OUT BY HOW MUCH % THE INCOME OF A IS GREATER

THAN B ?

**SOLUTION**

= (40/60)*100 =66.66%

Q 4. A WATCH COST RS 5000, FIRST PRICE INCREASE BY 20%

AND THEN DECREASE BY 20% AND DECREASE BY 10%, THEN

FIND NET LOSS OR PROFIT % ?

**SOLUTION**

= +20-10-(20*10/100)

=10-2

=8%

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