Gmat prep quants doubts!

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nitesh_2110: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Jul 25, 2010 2:51 am

Gmat prep quants doubts!

by nitesh_2110 » Thu Dec 23, 2010 5:00 am

I have my gmat appointment in less than two weeks!.. can someone pls post an explanation fr the 4 Qs!
all the four are frm GMAT prep!.

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Source: Beat The GMAT — Problem Solving | Thu Dec 23, 2010 5:00 am

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

by Anurag@Gurome » Thu Dec 23, 2010 5:16 am

Question Number 1

Point P and Q lies on the same circle with center at (0, 0).
Thus, (sÂ² + tÂ²) = (-âˆš3)Â² + 1Â² = 3 + 1 = 4

Again line segments OP and OQ are perpendicular.
Thus (slope of OP)*(slope of OQ) = -1

Slope of OP = 1/(-âˆš3) = -(1/âˆš3)
=> Slope of OQ = (t - 0)/(s - 0) = t/s = (-1)/(-1/âˆš3) = âˆš3
=> t = âˆš3s

Thus, (sÂ² + (âˆš3s)Â²) = 4
=> (sÂ² + 3sÂ²) = 4
=> sÂ² = 1
=> s = Â±1

As point Q lies in the first quadrant s = 1.

The correct answer is B.

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GMAT/MBA Expert

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

by Anurag@Gurome » Thu Dec 23, 2010 5:20 am

Question Number 2:

Remember that âˆš(xÂ²) is always a positive quantity. Thus for positive x, its value is x but for negative x, its value is -x i.e. in other words it is equal to |x|.

Thus, âˆš(xÂ²)/x = |x|/x

The correct answer is E.

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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 am; Location: Bangalore, India; Thanked: 146 times; Followed by:24 members

by shovan85 » Thu Dec 23, 2010 5:23 am

nitesh_2110 wrote:

As per the 4th one:

Maximum 4 letter code can be generated by using the 26 alphabets = 26^4
Maximum 5 letter code can be generated by using the 26 alphabets = 26^5

Thus, Total maximum = (Maximum 4 letter code can be generated) + (Maximum 5 letter code can be generated)
= 26^4 + 26^5
=26^4(1+26)
= 27(26^4)

IMO C

If the problem is Easy Respect it, if the problem is tough Attack it

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GMAT/MBA Expert

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

by Anurag@Gurome » Thu Dec 23, 2010 5:30 am

Question Number 3:

Let's analyze each of the options individually:

1. (a + b)Â² â‰ (aÂ² + bÂ²) => f(a + b) â‰ f(a) + f(b)
2. (a + b + 1) â‰ (a + 1) + (b + 1) = (a + b + 2) => f(a + b) â‰ f(a) + f(b)
3. âˆš(a + b) â‰ (âˆša + âˆšb) => f(a + b) â‰ f(a) + f(b)
4. 2/(a + b) â‰ (2/a) + (2/b) = 2(a + b)/ab => f(a + b) â‰ f(a) + f(b)
5. (-3(a + b)) = (-3a) + (-3b) => f(a + b) = f(a) + f(b)

The correct answer is E.

Quote

GMAT/MBA Expert

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

by Anurag@Gurome » Thu Dec 23, 2010 5:35 am

Question Number 4:

Maximum number of codes that can be generated = (Maximum number of 4-letter code) + (Maximum number of 5-letter code)

As there is no restrictions regarding repetition of letters,