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Question 1 of 5
1. Question
Find the number of numbers between 200 and 300, both included, which are not divisible by 2, 3, 4 and 5.
Correct
Answer : b
Use the principal of counting given in the theory of the chapter. Start with 101 numbers (i.e. all numbers between 200 and 300 both included) and subtract the number of numbers which are divisible by 2 (viz. (300200)/2]+ 1 = 51 numbers), the number of numbers which are divisible by 3 but not by 2 (Note: This would be given by the number of terms in thee series 201, 207,.. 297. This series has 17 terms) and the number of numbers which are divisible by 5 but not by 2 and 3. (The numbers are 205, 215, 235, 245, 265, 275, 295. A total of 7 numbers) Thus, the required answer is given by 1015117 – 7= 26. Option (b) is correct.
Incorrect
Answer : b
Use the principal of counting given in the theory of the chapter. Start with 101 numbers (i.e. all numbers between 200 and 300 both included) and subtract the number of numbers which are divisible by 2 (viz. (300200)/2]+ 1 = 51 numbers), the number of numbers which are divisible by 3 but not by 2 (Note: This would be given by the number of terms in thee series 201, 207,.. 297. This series has 17 terms) and the number of numbers which are divisible by 5 but not by 2 and 3. (The numbers are 205, 215, 235, 245, 265, 275, 295. A total of 7 numbers) Thus, the required answer is given by 1015117 – 7= 26. Option (b) is correct.

Question 2 of 5
2. Question
Given x and n are integers,(15 n3 + 6n^{2} + 5n + x)/n is not an integer for what condition?
Correct
Answer : c
Since 15n^{3}, 6n^{2} and 5n would all be divisible by n, the condition for the expression to not be divisible by n would be if x is not divisible by n. Option (c) is correct.
Incorrect
Answer : c
Since 15n^{3}, 6n^{2} and 5n would all be divisible by n, the condition for the expression to not be divisible by n would be if x is not divisible by n. Option (c) is correct.

Question 3 of 5
3. Question
The unit digit in the expression 36^{234}*33^{512}*39^{180}– 54^{29}*25^{123}*31^{512} will be
Correct
Answer : C
It can be seen that the first expression is larger than the second one. Hence, the required answer would be given by the (units digit of the first expression – units digit of the second expression)= 60 =6.
Option (c) is correct.
Incorrect
Answer : C
It can be seen that the first expression is larger than the second one. Hence, the required answer would be given by the (units digit of the first expression – units digit of the second expression)= 60 =6.
Option (c) is correct.

Question 4 of 5
4. Question
The difference of 10 ^{25} – 7 and 10^{24 } + x is divisible by 3 for x = ?
Correct
Answer : b
Suppose you were to solve the same question for
10^{3 } – 7 and 10^{2} +x
10^{3}7= 993 and 10^{2} +x= 100 +x.
Difference = 893 x
For 10^{4} – 7 and 10^{3} +x
The difference would be 9993(1000 + x) = (8993x)
For 10^{4} and 10^{3} +x
Difference: 99993 (10000 + x) = (89993x)
You should realize that the difference for the given question would be 8999 ………..9 3 – x . For this difference to be divisible by 3, x must be 2 (since that is the only option which will give you a sum of digits divisible by 3).
Incorrect
Answer : b
Suppose you were to solve the same question for
10^{3 } – 7 and 10^{2} +x
10^{3}7= 993 and 10^{2} +x= 100 +x.
Difference = 893 x
For 10^{4} – 7 and 10^{3} +x
The difference would be 9993(1000 + x) = (8993x)
For 10^{4} and 10^{3} +x
Difference: 99993 (10000 + x) = (89993x)
You should realize that the difference for the given question would be 8999 ………..9 3 – x . For this difference to be divisible by 3, x must be 2 (since that is the only option which will give you a sum of digits divisible by 3).

Question 5 of 5
5. Question
Find the value of x in
Correct
Answer : b
The value of x should be such that the left hand side after completely removing the square root signs should be an integer. For this to happen, first of all the square root of 3x should be an integer, Only 3 and 12 from the options satisfy, this requirement. If we try to put x as 12, we get the square root of 3 as 6. Then the next point at which we need to remove the square root sign would be 12+2(6) = 24 whose square root would be an irrational number. This leaves us with only 1 possible value (r = 3). Checking for this value of x we can see that the expression is satisfied as LHS = RHS.
Incorrect
Answer : b
The value of x should be such that the left hand side after completely removing the square root signs should be an integer. For this to happen, first of all the square root of 3x should be an integer, Only 3 and 12 from the options satisfy, this requirement. If we try to put x as 12, we get the square root of 3 as 6. Then the next point at which we need to remove the square root sign would be 12+2(6) = 24 whose square root would be an irrational number. This leaves us with only 1 possible value (r = 3). Checking for this value of x we can see that the expression is satisfied as LHS = RHS.
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