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Question 1 of 5
1. Question
AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 943. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 6, then what is A + B + C equal to?
Correct
Answer: C
Solution:
Given that,
AB and CD are 2-digit numbers.
Multiplying AB with CD results in a 3-digit number DEF.
Adding DEF to another 3-digit number GHI results in 943.
A, B, C, D, E, F, G, H, I are distinct digits.
E = 0, F = 6
Now,
We need a product of the form D06.
Try the pair that gives 406: AB = 29 and CD = 14.
This satisfies D = 4 (units of CD) and DEF = 406 with E = 0 and F = 6.
Check the sum:
DEF + GHI = 943 ⇒ 406 + GHI = 943 ⇒ GHI = 537.
Digits used are A=2, B=9, C=1, D=4, E=0, F=6, G=5, H=3, I=7 — all distinct.
Therefore, A + B + C = 2 + 9 + 1 = 12
Hence option (c) is correct.
Incorrect
Answer: C
Solution:
Given that,
AB and CD are 2-digit numbers.
Multiplying AB with CD results in a 3-digit number DEF.
Adding DEF to another 3-digit number GHI results in 943.
A, B, C, D, E, F, G, H, I are distinct digits.
E = 0, F = 6
Now,
We need a product of the form D06.
Try the pair that gives 406: AB = 29 and CD = 14.
This satisfies D = 4 (units of CD) and DEF = 406 with E = 0 and F = 6.
Check the sum:
DEF + GHI = 943 ⇒ 406 + GHI = 943 ⇒ GHI = 537.
Digits used are A=2, B=9, C=1, D=4, E=0, F=6, G=5, H=3, I=7 — all distinct.
Therefore, A + B + C = 2 + 9 + 1 = 12
Hence option (c) is correct.
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Question 2 of 5
2. Question
A 3-digit number ABC, on multiplication with D gives 42DD where A, B, C and D are different non-zero digits. What is the value of A+B+C?
Correct
Answer: C
Solution:
Given that,
A 3-digit number ABC, on multiplication with D gives 42DD
A, B, C and D are different non-zero digits.
Now,
We need a product of the form 42DD
Check possible D so that 42DD divided by D gives a valid 3-digit ABC with all digits distinct and none equal to D.
If D = 8, then 4288/8 = 536
A = 5, B = 3, C = 6 are distinct, none equals D
If D = 6, then 4266/6 = 711 (digits repeat, not allowed)
If D = 7, then 4277/7 = 611 (digits repeat, not allowed)
Other D values give invalid or non-distinct cases
Therefore, ABC = 536 and A + B + C = 5 + 3 + 6 = 14
Hence option (c) is correct
Incorrect
Answer: C
Solution:
Given that,
A 3-digit number ABC, on multiplication with D gives 42DD
A, B, C and D are different non-zero digits.
Now,
We need a product of the form 42DD
Check possible D so that 42DD divided by D gives a valid 3-digit ABC with all digits distinct and none equal to D.
If D = 8, then 4288/8 = 536
A = 5, B = 3, C = 6 are distinct, none equals D
If D = 6, then 4266/6 = 711 (digits repeat, not allowed)
If D = 7, then 4277/7 = 611 (digits repeat, not allowed)
Other D values give invalid or non-distinct cases
Therefore, ABC = 536 and A + B + C = 5 + 3 + 6 = 14
Hence option (c) is correct
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Question 3 of 5
3. Question
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits and ABC + DEF = 1000, then what is the value of A+B+C+D+E+F?
Correct
Answer: B
Solution:
Given that,
ABC and DEF are both 3-digit numbers with distinct non-zero digits and ABC + DEF = 1000
Now, taking values ABC = 124 and DEF = 876, 124 + 876 = 1000
So, A + B + C + D + E + F = 1 + 2 + 4 + 8 + 7 + 6 = 28
Hence option (b) is correct
Incorrect
Answer: B
Solution:
Given that,
ABC and DEF are both 3-digit numbers with distinct non-zero digits and ABC + DEF = 1000
Now, taking values ABC = 124 and DEF = 876, 124 + 876 = 1000
So, A + B + C + D + E + F = 1 + 2 + 4 + 8 + 7 + 6 = 28
Hence option (b) is correct
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Question 4 of 5
4. Question
Number 248 is added to 3B5 and the sum obtained is 5A3, where A and B are integers. It is given that 5A3 is exactly divisible by 3.
The only possible value of B isCorrect
Answer: A
Solution:
Given that,
Number 248 is added to 3B5 and the sum obtained is 5A3
A and B are integers
5A3 is exactly divisible by 3
Now,
Units: 5 + 8 = 13, write 3 and carry 1
Tens: B + 4 + 1 = B + 5, this equals A, and since hundreds must be 5 from 3 + 2 + 0, there is no carry here, so B + 5 < 10
Divisibility by 3: 5 + A + 3 = 8 + A must be divisible by 3, so A can be 1, 4, or 7
Since A = B + 5 and B + 5 < 10, A is in {5,6,7,8,9}. Intersection with {1,4,7} gives A = 7, hence B = 2
Thus B = 2
Hence option (a) is correct
Incorrect
Answer: A
Solution:
Given that,
Number 248 is added to 3B5 and the sum obtained is 5A3
A and B are integers
5A3 is exactly divisible by 3
Now,
Units: 5 + 8 = 13, write 3 and carry 1
Tens: B + 4 + 1 = B + 5, this equals A, and since hundreds must be 5 from 3 + 2 + 0, there is no carry here, so B + 5 < 10
Divisibility by 3: 5 + A + 3 = 8 + A must be divisible by 3, so A can be 1, 4, or 7
Since A = B + 5 and B + 5 < 10, A is in {5,6,7,8,9}. Intersection with {1,4,7} gives A = 7, hence B = 2
Thus B = 2
Hence option (a) is correct
-
Question 5 of 5
5. Question
Fungi are among the most diverse organisms on Earth, ranging from microscopic yeasts to large mushrooms. Neither plants nor animals, they occupy a unique kingdom and play crucial ecological roles. They act as decomposers, recycling nutrients from dead organic matter, and form symbiotic relationships with plants through mycorrhizal associations, enhancing soil fertility. Humans have long depended on fungi for bread, wine, antibiotics like penicillin, and industrial enzymes. Yet, fungi can also be harmful—causing crop diseases, food spoilage, and infections in humans. The study of fungi, called mycology, reveals their dual nature: they are both life-sustaining and life-threatening. Understanding fungi is essential for medicine, agriculture, and environmental sustainability.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?
Correct
Answer: (c)
Explanation:
Option (a) is incorrect: The passage highlights fungi’s harmful effects but equally emphasizes their benefits.
Option (b) is incorrect: It explicitly notes fungi are neither plants nor animals and have their own kingdom.
Option (d) is incorrect: The passage stresses fungi’s roles in antibiotics, enzymes, and agriculture.
Option (c) is correct: The passage conveys the dual nature of fungi—essential to human welfare but also capable of causing harm.Incorrect
Answer: (c)
Explanation:
Option (a) is incorrect: The passage highlights fungi’s harmful effects but equally emphasizes their benefits.
Option (b) is incorrect: It explicitly notes fungi are neither plants nor animals and have their own kingdom.
Option (d) is incorrect: The passage stresses fungi’s roles in antibiotics, enzymes, and agriculture.
Option (c) is correct: The passage conveys the dual nature of fungi—essential to human welfare but also capable of causing harm.








