Problem Solving

Hi dsuna,

please review the guidelines for posting...only supposed to post one question at a time!

I will answer your first question.

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

Before going crazy with setting up a bunch of equations, think about the problem and use the answer choices.

Thinking about the problem: we know there are a certain number of 7s and 77s that sum to 350. The question is asking for the number of 7s and 77s (whatever their ratio). If they were all 7s, you would have...50 7s (because 50*7=350). Because the answer choices run from 38-42, we know we have a lot of 7s, and that they can`t all be 7s.

Using the answer choices (because the GMAT is not a show-your-work exam): Start with answer choice C because it is clearly the easiest one to evaluate. 40*7=280. But, remember, they can`t all be 7s (because we would need 50 7s then). So if 39 of these 40 were 7s, we would have...one less 7 or 280-7=273. The other one would be 77 and 350-273 just happens to equal 77. Therefore, we have 39 7s and one 77. Done.

You could have also reasoned as follows. If 7 multiplied by a number equals another number whose units digits is zero, then the number being multiplied by 7 must be a multiple of 10. In other words, if 7*x= a number ending in zero, then x is a multiple of ten. Both 7 and 77 have 7 as their units digits. For a certain number of them to sum to 350, the number of them must be a multiple of ten. There is only one multiple of ten in the answer choices...choice C

Testluv wrote:Hi dsuna,

please review the guidelines for posting...only supposed to post one question at a time!

I will answer your first question.

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

Before going crazy with setting up a bunch of equations, think about the problem and use the answer choices.

Thinking about the problem: we know there are a certain number of 7s and 77s that sum to 350. The question is asking for the number of 7s and 77s (whatever their ratio). If they were all 7s, you would have...50 7s (because 50*7=350). Because the answer choices run from 38-42, we know we have a lot of 7s, and that they can`t all be 7s.

Using the answer choices (because the GMAT is not a show-your-work exam): Start with answer choice C because it is clearly the easiest one to evaluate. 40*7=280. But, remember, they can`t all be 7s (because we would need 50 7s then). So if 39 of these 40 were 7s, we would have...one less 7 or 280-7=273. The other one would be 77 and 350-273 just happens to equal 77. Therefore, we have 39 7s and one 77. Done.

You could have also reasoned as follows. If 7 multiplied by a number equals another number whose units digits is zero, then the number being multiplied by 7 must be a multiple of 10. In other words, if 7*x= a number ending in zero, then x is a multiple of ten. Both 7 and 77 have 7 as their units digits. For a certain number of them to sum to 350, the number of them must be a multiple of ten. There is only one multiple of ten in the answer choices...choice C

TestLuv, can you answer 5th question pls?

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

TestLuv, can you answer 5th question pls?

Hi!

Either the answer is between 0 and 6, and the OP mistranscribed or else the results of TV watching were not normally distributed...But an actual GMAT question would have made sure to tell the test-taker that the results were normally distributed. And since this was a GPrep question, the OP likely mistranscribed at least twice: failing to mention the word "normally" and mistranscribing either the mean or the correct answer choice.

. 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


The mean is 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.

i analyse this way 0 to 6 is 1 std dev.
6-12 is 2 std dev.
so pat will fall between 6 to 12.
m i right?

khushboo143 wrote:. 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


The mean is 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.

i analyse this way 0 to 6 is 1 std dev.
6-12 is 2 std dev.
so pat will fall between 6 to 12.
m i right?

Hi there,

...don't think so. It is clear from the English that the number of hours that "Pat...watched television...was below the mean."
And it was anywhere between 1 and 2 standard deviations below the mean. And the mean was 12. The problem with 12 is that 12 is not below 12!
Because the number of hours that Pat watched television was anywhere between one and two standard deviations below the mean, he was at least one and at most two standard deviations below the mean. The standard deviation is 6. This means he watched anywhere between 12-6 and 12-12 hours of television.

If the question had read "betwen zero and one standard deviations below", then 12 could have been a correct answer. Or, if the mean had been 21 instead, then 12 could have been a correct answer. The OP definitely mistranscribed somehwere in addition to the "matched".

Standard deviation is a measure of standard dispersal or "spreading out" from the mean. In your analysis, instead of subtracting 6 from the center or mean of 12, you are adding 6 to zero. That would make 12 itself two standard deviations away from itself!

sowree but is there a simple way to solve this sum ?
Standard deviation kinda freaks me out!