Number System
- The sum and product of two numbers are 11 and 18 respectively. The sum of their reciprocals is
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Let the numbers be x and y.
According to the question,
x + y = 11 ... (i)
xy = 18 ... (ii)
Dividing equation (i) by equation (ii)x + y = 1 + 1 = 11 xy y x 18 Correct Option: D
Let the numbers be x and y.
According to the question,
x + y = 11 ... (i)
xy = 18 ... (ii)
Dividing equation (i) by equation (ii)x + y = 1 + 1 = 11 xy y x 18
- The product of two numbers is 120 and the sum of their squares is 289. The sum of the
two numbers is
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Let the numbers be a and b.
According to the question,
ab = 120 ... (i)
and a2 + b2 = 289 ... (ii)
∴ (a + b)2 = a2 + b2 +2ab
= 289 + 2 × 120
= 289 + 240 = 529
∴ a + b = √529 = 23Correct Option: A
Let the numbers be a and b.
According to the question,
ab = 120 ... (i)
and a2 + b2 = 289 ... (ii)
∴ (a + b)2 = a2 + b2 +2ab
= 289 + 2 × 120
= 289 + 240 = 529
∴ a + b = √529 = 23
- In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attemtpts correctly is
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Let the number of correct answers be x.
∴ x × 4 – (75 – x ) × 1 = 125
⇒ 4x –75 + x = 125
⇒ 5x = 125 + 75 = 200∴ x = 200 = 40 5
Correct Option: B
Let the number of correct answers be x.
∴ x × 4 – (75 – x ) × 1 = 125
⇒ 4x –75 + x = 125
⇒ 5x = 125 + 75 = 200∴ x = 200 = 40 5
- In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number of questions, he answered correctly was
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If the number of correct answers be x, then
x × 4 – 1. (200 – x ) = 200
⇒ 4x – 200 + x = 200
⇒ 5x = 400⇒ x = 400 = 80 5 Correct Option: B
If the number of correct answers be x, then
x × 4 – 1. (200 – x ) = 200
⇒ 4x – 200 + x = 200
⇒ 5x = 400⇒ x = 400 = 80 5
- A farmer divides his herd of n cows among his four sons so that the first son gets one – half the herd, the second son gets one – fourth, the third son gets one – fifth and the fourth son gets 7 cows. The value of n is
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According to the question,
n + n + n 
+ 7 = n 2 4 5 ⇒ 10n + 5n + 4n + 7 = n 20 ⇒ 19n + 7 = n 20 ⇒ n − 19n = 7 ⇒ n = 7 20 20
⇒ n = 20 × 7 = 140Correct Option: C
According to the question,
n + n + n + 7 = n 2 4 5 ⇒ 10n + 5n + 4n + 7 = n 20 ⇒ 19n + 7 = n 20 ⇒ n − 19n = 7 ⇒ n = 7 20 20
⇒ n = 20 × 7 = 140
