Question

18. If the marked price of an article was 8400 and sold
for 6426 after offering two discounts one after the
other, the first being 15%, then the second discount
was
(1) 30%
(2) 20%
(3) 10%
(4) 12%
19. The difference between the greatest and smallest
perfect square number whose square root is a three
digit number, is
(1) 998001
(2) 978001
(3) 988001
(4) 10001
20. A shopkeeper has 5 red pens, x green pens and
8 black pens. If range of the data is a multiple of 7
and x is a two-digit prime number, then the sum of
digits of maximum possible value of xis
(1) 17
(2) 12
(3) 16
(4) 15​

Answer 1

Answer:

the required difference is 988001

Step-by-step explanation:

IN order to find the different between the greatest and the smallest perfect Square numbers with their square root being three digital numbers, we take the square first.

the greatest three digital number is 999

and it square is (999)²=998001 and the smallest three digit number is 100 and its squre is 10000

there for the require difference is 998001-10000=988001

Answer 2

Answer:

(18) Option (3) 10%

(19) Option (3) 988001

(20) Option (1) 17

Step-by-step explanation:

(18) Let the second discount be r%

After offering the first discount, the price of the article

$=8400-8400\times\frac{15}{100}$

$=8400-84\times 15$

$=8400-1260$

$=7140$

After offering the second discount, the price is 6426

Therefore,

$7140-7140\times\frac{r}{100}=6426$

$\implies 714\times\frac{r}{10}=714$

$\implies r=10$

Therefore, the second discount was 10%

(19) The greatest three digit number is 999 and the smallest is 100

$999^2-100^2=(999+100)(999-100)=1099\times 899=988001$

(20) Range of the data is Highest value - Lowest value

Since x is a two digit prime number

Therefore, x is the greatest number

Range will be x-5

x-5 should be divisible by 7

i.e. x when divided by 7 should give remainder 5

Two digit numbers divisible by 7 are

14, 21, 28, 35, 42, 49, 56,63, 70, 77, 84, 91, 98

Thus, x can be

14+5 = 19 (Prime)

21+5 =26 (Not prime)

28 + 5 = 33 (Not prime)

35 + 5 = 40 (Not Prime)

42 + 5 = 47 (Prime)

49 + 5 = 54 (Not prime)

56 + 5 = 61 (Prime)

63 + 5 = 67 (Prime)

70 + 5 = 75 (Not prime)

77 + 5 = 82 (Not prime)

84 + 5 = 89 (prime)

91 + 5 = 96 (Not prime)

Therefore, the highest value of x can be 89

The sum of the digits = 8 + 9 = 17

Thus, option (1) is correct.

Hope this helps.