Some help with specific PS questions

[ronm]

Hey all,

My exam is coming up soon and there are some specific questions that I am having trouble understanding.

I would really appreciate someone explaining the four questions below. Thank-you.

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5^12 x 4^11 = 2 x 1-^n What is the value of n?
ANS = 21

I worked this problem every way I can but I can't get 21. What is the method for solving this type problem with mixed exponents?
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cubed root of (x - b) = c^6
ANS = c^18 + b

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A college admissions officer predicts that 20% of the students who are accepted to college will not attend the college. According to this fact how many students should be accepted to achieve an enrollment of x students

ANS = 1.25x
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A certain list of 100 data elements has an average of 6 and a standard deviation of d, where d is positive.

Which of hte following pairs of data, when added to the list, must result in a list of 102 data elements with a standard deviation less than d.

-6 0
0 0
0 6
0 12
6 6

ANS 6 6
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Thanks for you help here

[dmateer25]

5^12 x 4^11 = 2 x 1-^n What is the value of n?
ANS = 21

I think you typed the problem wrong. I have seen this in the past and believe it should be:

5^21 x 4^11 = 2 x 10^n

5^21 x 2^22 = 2 x 2^n x 5^n

5^21 x 2^22 = 2^n+1 x 5^n

21 = n

[pbanavara]

For the rest:

2. Cube on both sides u'll get x-b = c^3, so x = c^3+b

3. 20% of students who do not attend college = x . Let y students be admitted to the college.

so y - y/5 = x => y = 1.25x

Sorry can't solve the SD problem. I'm still getting over my aversion with standard deviation.

- pradeep

[RideGMAT]

The SD problem is basically testing your understanding of the meaning of deviation.

For any data group, given mean, SD tells you how dispersed the data is. I.e., if SD is more, the data is more dispersed, and if SD is less, data elements are located closer to the mean. (image 2 bell shapped curves with same mean, but the one with higher SD is more spread out)

With this understanding of SD, look at what the Q is asking:
For a data group containing 100 elements, the mean is 6. The examiner is asking you to select 2 elements that will decrease the SD.
You can select any 2 elements that lie closest to the mean.

From the answer choices, (E) best satisfies as an answer, since both the elements are closest to the mean.

Mathematically,

SD = root of [(∑(x – 6)^2) / 100]
You are asked to add 2 data elements (let them be a & b for now):
Therefore, SD = root of [(∑(x – 6)^2 +(a-6)^2 + (b-6)^2)/ 102]

The Q also says, SD should decrease: Given that denominator has increased marginally, SD will decrease when numerator decreases or remains constant.

Key in the answer choices in the above formula and compare:

(A) Numerator increases by 144, reject
(B) Numerator increases by 36*36, reject
(C) Numerator increases by 144, reject
(D) Numerator increases by 36*36, reject
(E) Numerator remains unchanged, CORRECT