Need help with these Maths Questions

Question 1:

If we know two sides of a triangle, then 3rd side of the triangle lies between the difference and sum of the two given sides of the triangle.
So, 5 - 2 < 3rd side < 5 + 2
3 < 3rd side < 7
Since the 3rd side lies between 3 and 7, so 3 + 2 + 5 < perimeter < 7 + 2 + 5
or 10 < perimeter < 14

[spoiler]The correct answer is A; none.[/spoiler]

Question 2:

We know, probability = No. of favorable outcomes/ Total no. of outcomes
Here total no. of outcomes = 25

(1) There are no white balls with an even no., so (1) is NOT SUFFICIENT.

(2) P(White) - P(Even) = 0.2 and since there are 25 balls in total, so white balls - even balls = 0.2 *25 = 5. But there can be many possibilities when the difference of white balls and even balls is 5. So, there is no unique answer and hence (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), we have again have no. of combinations, so combining also is NOT SUFFICIENT.

[spoiler]The correct answer is E.[/spoiler]

Question 3:

Let the mean = x and 1 standard deviation = y.
Then x - 2y = 58
x + 3y = 98

Solving the 2 equations we get, 5y = 40 or y = 8, which implies x = 74

[spoiler]The correct answer is A.[/spoiler]

Question 4:

y = (x + a)(x + b) = x^2 + (a + b)x + ab

(1) a + b = -1 implies y = x^2 - x + ab, which is NOT SUFFICIENT.

(2) The graph intersects at (0, -6) implies -6 = ab (by putting x = 0 and y = -6), which is NOT SUFFICIENT.

Combining (1) and (2), we get y = x^2 - x - 6, which is SUFFICIENT.

[spoiler]The correct answer is C.[/spoiler]

Question 5:

Since the integers are consecutive, so if we know any one of the 11 integers, then the question can be answered.

(1) The average of first 9 integers is 7 implies 7 = (sum of first 9 integers)/9
or Sum of first 9 integers = 7 * 9 = 63, which is SUFFICIENT as only one set of 1st nine integers will give an average of 7. Therefore, we can find the average of first 11 consecutive integers. Hence, SUFFICIENT.

(2) Average of last 9 integers is 9 implies 9 = (sum of last 9 integers)/9
or Sum of last 9 integers = 9 * 9 = 81, which is SUFFICIENT as only one set of last nine integers will give an average of 9. Therefore, we can find the average of first 11 consecutive integers. Hence, SUFFICIENT.

[spoiler]The correct answer is (D).[/spoiler]

Question 6:

(1) (x + y) < 20. Since we have one equation we 2 unknowns, so (1) is NOT SUFFICIENT.

(2) y < 20 is again NOT SUFFICIENT as we don't know the relation between x and y.

Combining (1) and (2), we have x + y < 20 and y < 20.
If y = -20 and x = 25, here x > 20
If y = 20 and x = -10, here x < 20, so we don't get a unique answer.

Combining the two statements also is NOT SUFFICIENT.

[spoiler]The correct answer is E.[/spoiler]

Question 7:

(1) alone is NOT SUFFICIENT.
(2 alone is NOT SUFFICIENT.

Combining (1) and (2), we get the following figure:



In triangle PRT, (180 - 2y) + (180 - 2z) + 90 = 180 implies y + z = 135...Equation (1)

In PQSU, (180 - y) + x + (180 - z) + 90 = 360 implies x = y + z - 90...Equation (2)

Solving equations (1) and (2), x = 135 - 90 = 45º

[spoiler]The correct answer is C.[/spoiler]