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GMAT Prep 6 questions – I don't know how to solve them

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GMAT Prep 6 questions – I don't know how to solve them

by dsuna » Mon Mar 19, 2007 9:10 am
Hi,
I have my GMAT exam next week and I don't know how to solve these problems. Is anyone who can help me understand them? Thanks a lot.

1. In each term in the sum a1 + a2 + …..+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
38, 39, 40, 41, 42 following math problems. Is anyone who can help me understand
Ans. 40

2. In the XY-plane, at what two points does the graph of the y=(x+a)(x+b) intersect the x-axis?
1.a+b = -1
2.The graph intersect the y-axis at (0,-6)

Ans. Both statements TOGETHER are sufficient, but NEITHER….

3. For every integer K from 1 to 10, inclusive, the Kth term of a certain sequence is given by (-1)^(k+1)* (1/2k) if T is the sum of the first 10 terms in the sequence the T is:
Greater than 2
Between 1 and 2
Between ½ and 1
Ans.: Between ¼ and ½
Less than 4

4. In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Ans. 0.70

5. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Ans. 12

6. Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously can fill the tank in 3/2 hours, and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously to fill the tank?

Ans. 1
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Question 1

by rjfNC » Tue Mar 20, 2007 6:57 am
Question 1
If the series sum is equal to 350 you can break up the summation into two factors. 7a+77b = 350
a = the number of 7's in the series
b = the number of 77's in the series

you also know that the sum of a and b is the answer. We'll call the answer z so:
a+b = z

With two equations you have two unknowns with one guessed solution.
7a + 77b = 350
a+b = z

combining equations gives you
(z-b)7 + 77b = 350
7z + 70b = 350
z = 50 - 10b

you can now guess the answer but you can see, since b has be to an integer, that 40 would be the only answer.
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Re: GMAT Prep 6 questions – I don't know how to solve them

by gabriel » Tue Mar 20, 2007 10:25 am
dsuna wrote:Hi,
I have my GMAT exam next week and I don't know how to solve these problems. Is anyone who can help me understand them? Thanks a lot.

1. In each term in the sum a1 + a2 + …..+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
38, 39, 40, 41, 42 following math problems. Is anyone who can help me understand
Ans. 40

2. In the XY-plane, at what two points does the graph of the y=(x+a)(x+b) intersect the x-axis?
1.a+b = -1
2.The graph intersect the y-axis at (0,-6)

Ans. Both statements TOGETHER are sufficient, but NEITHER….

3. For every integer K from 1 to 10, inclusive, the Kth term of a certain sequence is given by (-1)^(k+1)* (1/2k) if T is the sum of the first 10 terms in the sequence the T is:
Greater than 2
Between 1 and 2
Between ½ and 1
Ans.: Between ¼ and ½
Less than 4

4. In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Ans. 0.70

5. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Ans. 12

6. Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously can fill the tank in 3/2 hours, and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously to fill the tank?

Ans. 1

1.) 7x + 77y = 350.... x+11y=50

theerfore.... y = (50 - x)/11... therefore x will be of the form 11a + 6.... therfore differnt values of x = 6,17,28,39,50.... u will find that at x=39.. y=1 and x+y=40


2.)this q has already been answered in the DS section..

3.) alrite for k = 1.. the first no. of the sequence is (-1)^2*1/2 = 1/ 2.. similarly the 2nd term of the sequence ( for k=2) is (-1)^3*1/4..
So the sequence will be .. 1/2 - 1/4+ 1/ 6 - 1/8 + 1/10 - 1/12+ 1/14-1/16+1/18-1/20 ... calculate and the value shuld be somewhre between 1/4 and 1/2

4.)take the total no. of students as 1000... then apply all the given percentages and u will get that the no. of students who are 25 years or older... as 276.. therfore the total no of students below 25 is 724... and therefore the probability is 724/1000... 0.724

5.) still working on this one..

6.)let the total amount of work done be 120 units... therfore the amt of work done by a & b in one hr is 120/6/5= 100... a&c 120/3/2 = 80... b & c = 120/2 =60..... 2 ( a+b+c )= 240... a+b+c=120... the amt of work done in one hr by all three is 120 units... therefore working together they will take 1 hr...
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Nr5

by patrik.herzog » Wed Mar 21, 2007 6:53 am
Nr 5 is quite easy. The mean should be 21 (instead of 12)
21 - 6 = 15 (6 = 1 Standard Deviation)
21 - 12 = 9 (12 = 2 Standard Deviations)

So, Pat watch between 9 and 15 hours TV last week. (Ans > 12)
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by Cybermusings » Tue Mar 27, 2007 10:19 am
Lets start with 1

1)1. In each term in the sum a1 + a2 + …..+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
38, 39, 40, 41, 42 following math problems. Is anyone who can help me understand

Note the sequence : 7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140

Hence it is very clear that '0' would be there at the units place only when 7 is multiplied by multiples of 10 viz., 10,20, 30, 40 and so on

Thus 40 is the answer
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by Cybermusings » Tue Mar 27, 2007 10:29 am
4. In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Ans. 0.70

Assume 10,000 students

4,800 males and 5,200 females

60% of males below 25

= 4800 * 60/100 = 2880

80% of males below 25

= 5,200 * 80/100 = 4160

Total = 7040

Therefore probablity = 7040 / 10000 = .704 = .7 approx

NOTE FOR QUESTION 5 CAN YOU PLEASE SPECIFY THE ANSWER CHOICES?
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by Cybermusings » Tue Mar 27, 2007 10:30 am
For explanation of Question 6 ...Gabriel has explained it pretty well
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Re: GMAT Prep 6 questions – I don't know how to solve them

by daylebo5 » Fri Jul 17, 2009 3:03 am
dsuna wrote:Hi,
3. For every integer K from 1 to 10, inclusive, the Kth term of a certain sequence is given by (-1)^(k+1)* (1/2k) if T is the sum of the first 10 terms in the sequence the T is:
Greater than 2
Between 1 and 2
Between ½ and 1
Ans.: Between ¼ and ½
Less than 4
Ans. 1
I too had a problem with this question... however can it be solved as below or is it a typo in the gmatprep...

3. For every integer K from 1 to 10, inclusive, the Kth term of a certain sequence is given by (-1)^(k+1)* (1/2^k) if T is the sum of the first 10 terms in the sequence the T is:
Greater than 2
Between 1 and 2
Between ½ and 1
Between ¼ and ½
Less than 4
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by ghacker » Fri Jul 17, 2009 10:31 am
1. In each term in the sum a1 + a2 + …..+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

How can we make 350 from 7 and 77 only we know that we cannot make 350 from 77 alone but we can make 350 from 7 ;350= 7*50 hence the max that n can take is 50( in this case it can't be 50 since we need to have 77 also)

77 = 7*11 and 7 = 7*1 but 350 is even

so 350 = even hence n must be always even ; so 39 and 41 are out

this leaves 38 , 40 and 42

there should be a zero in the units place .

0 = 3+7 but 3 = 9*7

and the contribution to the unit digit from 77 = > 7 , 4, 1


so their must be a 9 and the other must also be odd so 38 and 42 are out

Only answer is 40

that is 39*7+77*1 = 350
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by truplayer256 » Fri Jul 17, 2009 12:31 pm
I solved question #6 like this:

1/A+1/B=5/6---(1)

1/A+1/C=2/3---(2)

1/B+1/C=1/2---(3)

(2)-(3)=1/A-1/B=1/6---(4)

(4)+(1)=2/A=1

A=2

Now substitute A into equations 1, 2, 3, or 4 to get B and C.

B=3

C=6

1/A+1/B+1/C=1/X

X= The number of hours it takes pumps A, B, and C, operating simultaneously to fill the tank

1/2+1/3+1/6=1/X

1=1/X

X=1 hour.
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#4.

by AndreaV424 » Fri Jul 17, 2009 3:43 pm
#4.

lets say 100 students:

48 male
52 female

40% of male would be 19.2
20% of female woud be 10.4

Approximately 29 are 25 or older, meaning there are 71 people under 25.

71/100 = .71 (closest to .7)
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by alexdallas » Sat Aug 08, 2009 4:44 pm
For problem 3:
there's gotta be a faster way to do it, right?

could we use the Sum of an arithm. progression formula somehow?
sum = N/2 * (A1 + An)

did anyone solve it this way, or another way?
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by prindaroy » Sat Aug 08, 2009 8:31 pm
for no. 3, you can use formula for a geometric sequence with r = -1/2

sum of geometric sequence = a((r^n+1) - 1)/1 - r

For no.1 it's really easy....what is 350 - 77 = 273. is 273 divisible by 7? yes by 39. so there are 39 7s and 1 77. If that wasn't the case then 350 - 77 - 77..and you get some other number, check if that is divisible by 7...so on and so forth. this is the fastest way to do it
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by real2008 » Sun Aug 09, 2009 6:09 am
5. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Ans. 12


for this qn i feel the answer should between 0 & 6
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by crackgmat007 » Wed Oct 28, 2009 10:41 am
real2008 wrote:5. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Ans. 12


for this qn i feel the answer should between 0 & 6
I think so.

Anyone?
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