Quantitative Aptitude - Arithmetic Ability Questions

Given word is THERAPY.

Number of letters in the given word = 7

Number of vowels in the given word = 2 = A & E

Required number of different ways, the letters of the word THERAPY arranged such that vowels always come together is

6! x 2! = 720 x 2 = 1440.

In the given options,

12/49 can be written as 1/(49/12) = 1/4.083

7/30 can be written as 1/(30/7) = 1/4.285

13/56 can be written as 1/(56/13) = 1/4.307

11/46 can be written as 1/(46/11) = 1/4.1818

Here in the above,

1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.

Given, difference of the squares of two numbers is 180.

= k² - l² - 180

Also, square of the smaller number is 8 times the larger.

= l² = 8k

Thus, k² - 8a - 180 = 0

k² – 18k + 10k - 180 = 0

→  k(k - 18) + 10(k – 18) = 0

= (k + 10)(k – 18) = 0

→  k = -10, 18

Thus, the other number is

324 - 180 = l² 

→ Numbers are 12, 18 or -12, 18.

20% of 120

20 x 120/100

= 4 x 6

= 24

Hence, 20% of 120 = 24.

3x2 – 14x + 16=0

3x2 –6x – 8x + 16=0

3x (x-2) – 8 (x-2)

(3x-8) (x-2)=0

x=8/3 or 2

5y2 – 16y + 12=0

5y2 – 10y – 6y + 12=0

5y (y-2) – 6 (y-2)=0

(5y-6) (y-2)=0

y=6/5 or 2

Can't be determined.