GMAT Prep! Questions!Help both PS&DS mixed!Exam on Monda

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1. h(n) is the product of the even numbers from 2 to n, inclusive, and p is the least prime factor of h(100)+1. What is the range of p?
Answer is p>40
DS
2. At least 100 students at a certain high school study Japanese. If 4 percent of the students who study French also study Japanese, do more students at the school study French than Japanese?
1). 16 students at the school study both French and Japanese.
2). 10 percent of the students at the school who study Japanese also study French.
OA is B
3. If it took Carol 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? ( 1mile=5,280feet)
1). The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
2). The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second
OA is E

4. . How many different prime numbers are factors of the positive integer n?
1). four different prime numbers are factors of 2n.
2). four different prime numbers are factors of n^2.
OA B

5. A certain list of 100 data has an average of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list 0f 102 data with standard deviation less than d?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

OA E

6.
Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000
The table above shows the total sales recorded in July for the five salespeople. It was discovered that one of Cal’s sales was incorrectly recorded as one of Ann’s sales. After this error was corrected, Ann’s total sales were still higher than Cal’s total sales, and the median of 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?

7. Circle C and line k lie in the xy-plane. If circle c is centered at the origin and has radius1, does line k intersect circle c?
1). the x-intercept of line k is greater than 1
2). the slope of line k is -1/10
OA E
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by aj5105 » Tue Jun 16, 2009 4:17 am
2.
From 1, 16 students study both French and Japanese, so 16/0.04=400 students study French, combine "at least 100 students study Japanese", insufficient.

From 2, we can know that, 10% Japanese studying students=4% French studying students.

Apparently, more students at the school study French than study Japanese.

(B)

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by aj5105 » Tue Jun 16, 2009 4:24 am
3. (E)

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by tohellandback » Tue Jun 16, 2009 9:55 pm
1)
h(100)=2*4*6*....*100=2(1*2*3*..50)
so it is clear that highest prime factor of h(100) is 47
now 47 will certainly not be a factor of h(100)+1
so the least prime factor will be>47 . so of course>40
The powers of two are bloody impolite!!

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by tohellandback » Tue Jun 16, 2009 10:27 pm
4)
B is correct
1) not sufficient. if a number 2n has 4 prime factors, number n can have 3 or four prime factors depending upon whether the number is even or odd
ex: n=105 has three prime factors 3,5,7
2n=210 has 4 prime factors-2,3,5,7

now take n=210, number has 4 prime factors
2n=420 also has 4 prime factors

2) sufficient. squaring doesn't change the number of prime factors, it just doubles their occurences
The powers of two are bloody impolite!!

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by Naruto » Wed Jun 17, 2009 12:19 am
5. A certain list of 100 data has an average of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list 0f 102 data with standard deviation less than d?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

IMO E

Well usually standard deviation formula is root of mean of square of deviation of each term from the average...putting it mathematically

d^2 = [(x1-6)^2+...(x100-6)^2]/100

(it just seems complicated) now logically for the new devaition to be less than d... or d^2 the denominator should increase and numerator either decrease or remain the same. That is possible with E only because the two terms added in that case would be zero and denominator will be 102 instead of 100.

Hope this is clear.

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by Naruto » Wed Jun 17, 2009 12:27 am
Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000
The table above shows the total sales recorded in July for the five salespeople. It was discovered that one of Cal’s sales was incorrectly recorded as one of Ann’s sales. After this error was corrected, Ann’s total sales were still higher than Cal’s total sales, and the median of 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?

IMO 120,000

Well for the median to be 330000, then only the value of Ann or Cal can be changed. Since its mentioned that after the correction Ann's sales are greater than Cal, therefore it can be assumed that Ann's sale is 330,000. Thus the change or correction is 450,000-330,000=120,000.

This can be cross checked by adding 120,000 to Cal's sales which makes it 310,000 i.e <330,000.

Hence the value of incorrectly recorded sale was 120,000.

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by abhinav85 » Thu Jun 25, 2009 9:53 am
Hey Can any one elaborate.........why the option is E.

I know its easy but i am just stuck with this problem.
5. A certain list of 100 data has an average of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list 0f 102 data with standard deviation less than d?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

IMO E

Well usually standard deviation formula is root of mean of square of deviation of each term from the average...putting it mathematically

d^2 = [(x1-6)^2+...(x100-6)^2]/100

(it just seems complicated) now logically for the new devaition to be less than d... or d^2 the denominator should increase and numerator either decrease or remain the same. That is possible with E only because the two terms added in that case would be zero and denominator will be 102 instead of 100.

Hope this is clear.

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by ssmiles08 » Thu Jun 25, 2009 10:18 am
abhinav85 wrote:Hey Can any one elaborate.........why the option is E.

I know its easy but i am just stuck with this problem.
you don't know what value d has been assigned to. For all you know it can be a really big standard deviation or very small deviation. To ensure that, the value of the 102 data points still fall below d is to maintain the same average as 6.

In (E) you are adding two data points which are 6's and the average of all the 102 data points still remains 6.

In all other choices, you are changing the average of data points by adding points greater or lower than the actual average.

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by abhinav85 » Thu Jun 25, 2009 10:48 am
Got it.........

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by missrochelle » Sun Aug 29, 2010 6:11 pm
got this problem on my gmat prep as my first question and was completely stumped! spent way to much time guessed A and moved on!