Need help with these Maths Questions

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earnest10: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sun Apr 25, 2010 1:37 pm; Thanked: 1 times

by earnest10 » Mon Feb 07, 2011 8:33 pm

Hello Forum,
I need help with theses maths questions. Thanks

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Source: Beat The GMAT — Problem Solving | Mon Feb 07, 2011 8:33 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 07, 2011 9:40 pm

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]

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by Anurag@Gurome » Mon Feb 07, 2011 9:53 pm

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]

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by Anurag@Gurome » Mon Feb 07, 2011 9:58 pm

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]

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by Anurag@Gurome » Mon Feb 07, 2011 10:07 pm

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]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 07, 2011 10:48 pm

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]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 07, 2011 10:54 pm

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]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Feb 07, 2011 11:16 pm

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 = 45Âº

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

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earnest10: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sun Apr 25, 2010 1:37 pm; Thanked: 1 times

by earnest10 » Tue Feb 08, 2011 3:05 pm

Thank you so much

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