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Question 1 of 5
1. Question
The sum of five consecutive numbers is 190. What is the sum of the largest and the smallest numbers?
Correct
Answer : c
Let the five consecutive numbers are
X – 2, x – 1, x, x + 1, x + 2.
Sum of numbers = 190
∴x – 2 + x – 1 +x +x + 1 + x + 2 = 190
5x = 190
X = 38
Sum of largest and smallest numbers = x + 2 + x -2 = 2x = 2 * 38 = 76
Incorrect
Answer : c
Let the five consecutive numbers are
X – 2, x – 1, x, x + 1, x + 2.
Sum of numbers = 190
∴x – 2 + x – 1 +x +x + 1 + x + 2 = 190
5x = 190
X = 38
Sum of largest and smallest numbers = x + 2 + x -2 = 2x = 2 * 38 = 76
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Question 2 of 5
2. Question
The difference between a two-digit number and the number obtained by interchangıng the two digits of the number is 18. The sum of the two digits of the number is 12. What is the product of the digits of two-digit number?
Correct
Answer : a
Let the unit’s digit be y and ten’s digit be x.
Then, the number = 10x + y
When interchanging the place, the number is 10y + x.
According to the question,
(10x+ y) – (10y + x) = 18
10 x + y -10y – x = 18
9x – 9y=18
X – y = 2
and x+y = 12
On adding Eqs. (1) and (2), We get
x = 7
∴ x = 7 and y = 5
Product = xy = 7 * 5 = 35
Incorrect
Answer : a
Let the unit’s digit be y and ten’s digit be x.
Then, the number = 10x + y
When interchanging the place, the number is 10y + x.
According to the question,
(10x+ y) – (10y + x) = 18
10 x + y -10y – x = 18
9x – 9y=18
X – y = 2
and x+y = 12
On adding Eqs. (1) and (2), We get
x = 7
∴ x = 7 and y = 5
Product = xy = 7 * 5 = 35
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Question 3 of 5
3. Question
Two trains are travelling in the same direction at 50 km/h and 30 km/h respectively. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train.
Correct
Answer : a
T = (LT+LO)/(ST-SO)
50-30 = 20km/hr=50/9 m/s
Now 18 = LT/(50/9)⇒LT = 100 m
Incorrect
Answer : a
T = (LT+LO)/(ST-SO)
50-30 = 20km/hr=50/9 m/s
Now 18 = LT/(50/9)⇒LT = 100 m
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Question 4 of 5
4. Question
The product of two consecutive odd numbers is 19043. Which is the smaller one?
Correct
Answer : a
Let the two consecutive odd numbers are x and x+2.
According to the question, x (x+2) = 19043
Incorrect
Answer : a
Let the two consecutive odd numbers are x and x+2.
According to the question, x (x+2) = 19043
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Question 5 of 5
5. Question
Let x and y be positive integers such that x˃y. The expression 3x + 2y and 2x +3y, when divided by 5 leave remainders 2 and 3, respectively. What is the remainder when (x-y), is divided by 5?
Correct
Answer : a
We have, 3x+2y is divided by 5 remainder is 2.
∴3x+2y=5q+2 ……………………..(1)
And 2x +3y is divided by 5 remainder is 3.
∴2x + 3y = 5m+3 ……………………..(2)
Subtract Eq. (2 ) from Eq.(1) , we get
x-y = 5(q-m)-1
x-y=5(q-m)-5+4
x-y=5(q-m-1)+4
∴x-y is divided by 5 remainder is 4.
Incorrect
Answer : a
We have, 3x+2y is divided by 5 remainder is 2.
∴3x+2y=5q+2 ……………………..(1)
And 2x +3y is divided by 5 remainder is 3.
∴2x + 3y = 5m+3 ……………………..(2)
Subtract Eq. (2 ) from Eq.(1) , we get
x-y = 5(q-m)-1
x-y=5(q-m)-5+4
x-y=5(q-m-1)+4
∴x-y is divided by 5 remainder is 4.
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