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Question 1 of 5
1. Question
The difference of cubes of two consecutive numbers is 3 less than the cube of the smaller number. What is the product of the two numbers?
Correct
Solution: A
Let the two consecutive numbers be ‘x’ and ‘x+1’.
As per given condition, (x+1)^3 – x^3 = x^3 – 3.
Formula: [a +b] ^3 = (a^3 + 3ba^2 + 3ab^2 + b^3)
Therefore, x^3 + 3x^2 + 3x + 1 – x^3 = x^3 – 3
- è x^3 – 3x^2 – 3x – 4 = 0
- è by trial and error we get x= 4, x+1= 5
Therefore product of such numbers = 4 * 5 = 20.
Hence, option (a) is correct.
Incorrect
Solution: A
Let the two consecutive numbers be ‘x’ and ‘x+1’.
As per given condition, (x+1)^3 – x^3 = x^3 – 3.
Formula: [a +b] ^3 = (a^3 + 3ba^2 + 3ab^2 + b^3)
Therefore, x^3 + 3x^2 + 3x + 1 – x^3 = x^3 – 3
- è x^3 – 3x^2 – 3x – 4 = 0
- è by trial and error we get x= 4, x+1= 5
Therefore product of such numbers = 4 * 5 = 20.
Hence, option (a) is correct.
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Question 2 of 5
2. Question
On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5?
Correct
Solution: D
Unconventional Method: Assume a smallest possible number, which when divided by 5 we get reminder of 3. The number is (5*0 +3)= 3
Now, 3 ^2 = 9.
By dividing 9 by 5 we get remainder of 4.
Hence, option (d) is correct
Formula Method:
Let the number be 5x+3.
Therefore, [(5x + 3)^2]/5= (25x^2 + 30x + 9)/5
- 25x^2/5 + 30 x/5 + 9/5
- Reminder will be 0+0+4= 4
Hence, option (d) is correct.
Incorrect
Solution: D
Unconventional Method: Assume a smallest possible number, which when divided by 5 we get reminder of 3. The number is (5*0 +3)= 3
Now, 3 ^2 = 9.
By dividing 9 by 5 we get remainder of 4.
Hence, option (d) is correct
Formula Method:
Let the number be 5x+3.
Therefore, [(5x + 3)^2]/5= (25x^2 + 30x + 9)/5
- 25x^2/5 + 30 x/5 + 9/5
- Reminder will be 0+0+4= 4
Hence, option (d) is correct.
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Question 3 of 5
3. Question
To five litre of 20% sulphuric acid, seven and half litre of 80% sulphuric acid is added. What is the strength of the acid in the mixture now?
Correct
Solution: A
Percentage strength of the acid in the mixture = Quantity (volume) of the acid in the mixture/Total volume × 100
= [(5*20/100) + (7.5*80/100)/(5+7.5)] *100 = (5*20+7.5*80) /(5+7.5) = 56%.Hence, option (a) is correct.
Incorrect
Solution: A
Percentage strength of the acid in the mixture = Quantity (volume) of the acid in the mixture/Total volume × 100
= [(5*20/100) + (7.5*80/100)/(5+7.5)] *100 = (5*20+7.5*80) /(5+7.5) = 56%.Hence, option (a) is correct.
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Question 4 of 5
4. Question
The average age of 60 students is 20 years. When 15 new students are admitted, the average increases by 0.4 years. What must be the average age of the new students?
Correct
Solution: A
Let the average age of the newly admitted 15 students be x years.
Therefore, total age of 15 newly admitted students = 15x
Since given average age of existing 60 students = 20
Therefore, total age of the existing 60 students = 60×20
Hence, total age of the 75 students = 60×20 + 15x
Since average after admission of new students increases by 0.4 years.So new average = 20.4 years
è 60×20 + 15x =75×20.4
è 1200 + 15x = 1530
è 15x = 1530-1200
è 15x = 330
è x = 330/15
è x = 22 yearsHence, option (a) is correct.
Incorrect
Solution: A
Let the average age of the newly admitted 15 students be x years.
Therefore, total age of 15 newly admitted students = 15x
Since given average age of existing 60 students = 20
Therefore, total age of the existing 60 students = 60×20
Hence, total age of the 75 students = 60×20 + 15x
Since average after admission of new students increases by 0.4 years.So new average = 20.4 years
è 60×20 + 15x =75×20.4
è 1200 + 15x = 1530
è 15x = 1530-1200
è 15x = 330
è x = 330/15
è x = 22 yearsHence, option (a) is correct.
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Question 5 of 5
5. Question
In New Delhi, the mean temperature from Tuesday to Thursday was 35°C and from Wednesday to Friday was 38°C. If the temperature on Friday was 25% higher than that on Tuesday, then the temperature in on Friday was:
Correct
Solution: A
Mean temperature from Tuesday to Thursday = 35°C
Therefore, (Tuesday + Wednesday +Thursday)/3 = 35°C
or total temperature of (Tuesday + Wednesday + Thursday = 105℃.. (Eq 1)Mean temperature from Wednesday to Friday = 38 ℃
Therefore, (Wednesday + Thursday + Friday)/3 = 38°C
or Total temperature of Wednesday + Thursday + Friday = 114 °C.. (Eq 2)By subtracting (Eq 2) – from Eq 1, we get:
Temperatures of (Friday – Tuesday) = 9 °C
Given that temperature on Friday was 25% higher than Tuesday
Therefore, Friday = 1.25 Tuesday
è Friday – Friday/1.25 = 9
è (1.25 Friday – Friday)/1.25 = 9
è 0.25 Friday = 9 x 1.25
è Friday = (9 x 1.25)/0.25
è Temperature of Friday = 45℃Hence, option (a) is correct.
Incorrect
Solution: A
Mean temperature from Tuesday to Thursday = 35°C
Therefore, (Tuesday + Wednesday +Thursday)/3 = 35°C
or total temperature of (Tuesday + Wednesday + Thursday = 105℃.. (Eq 1)Mean temperature from Wednesday to Friday = 38 ℃
Therefore, (Wednesday + Thursday + Friday)/3 = 38°C
or Total temperature of Wednesday + Thursday + Friday = 114 °C.. (Eq 2)By subtracting (Eq 2) – from Eq 1, we get:
Temperatures of (Friday – Tuesday) = 9 °C
Given that temperature on Friday was 25% higher than Tuesday
Therefore, Friday = 1.25 Tuesday
è Friday – Friday/1.25 = 9
è (1.25 Friday – Friday)/1.25 = 9
è 0.25 Friday = 9 x 1.25
è Friday = (9 x 1.25)/0.25
è Temperature of Friday = 45℃Hence, option (a) is correct.
