Problem Solving

Hello,

Can someone help me with these GMAT prep questions please? Thanks

1. The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the months of January is 3/5. If the fuel oil bill for February has been $40 more, the corresponding ratio would have been 5/3. How much was Alex's fuel oil bill for Jan? Ans is $240

2. In the infinite sequence of (please note these are sub powers, the small text feature is not working) a1, a2, a3,.....an, each term after the first is equal to twice the previous term. If a5 - a3 = 12, what is the value of a1? Answer is 12/7

Hello- These are some additional questions--if someone can help me with these before 1pm EST, I'd be very grateful:)) thank you!

3. If two of the 4 expressions x+y, x+5y, x-y and 5x-y are chosen at random, what is the probability that their product will be of the form of x^2- (by)62, where b= integer? Ans is 1/6

4.
For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6-n points whenever one of it's members finished in nth place where 1< equal to n < or equal to 5. There were no ties, disqualifications or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?


5. For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3 since 75=3*5*5. How many two digit positive integers have length 6? Ans is 2 (what is the fastest way to do this?)

6. A certain meter records between 0 and 10 volts inclusive. If the average (arithmetic mean) value of 3 recordings on the meter was 8 volts, what was the smallest possible recording in volts?
Ans is 4

Bschool08 wrote: 6. A certain meter records between 0 and 10 volts inclusive. If the average (arithmetic mean) value of 3 recordings on the meter was 8 volts, what was the smallest possible recording in volts?
Ans is 4

Not sure if this is the best way to do it

Let x=smallest possible value

(x +y+z) / 3 = 8
x+y+Z = 24

for smallest value, maximise the other two values hence y,z=10

Therefore,

x+20=24
Giving x = 4.

Thanks HarvardDreamin! I don't know what the actual explanation is but what you've explained seems to make sense:)

1. F:J = 3:5 and (F+40):J = 5:3 ---> Solve these two equs.

2. First term = a
Second term = 2a
:
:
:
Fifth term = 2^4a
So 2^4a - 2^2a = 12
or 4a(4 - 1) = 12
or a = 1
But I don't know why the answer is 12/7. Am I missing something?

3. Already discussed in the forum. Pls search.

4. Not confident enough! Is the answer - 6?

camitava wrote:1. F:J = 3:5 and (F+40):J = 5:3 ---> Solve these two equs.

I tried that for the first one but didnt get 240..Do you mind showing your working if it works for you ? Thx

4.
For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6-n points whenever one of it's members finished in nth place where 1< equal to n < or equal to 5. There were no ties, disqualifications or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?




Not sure but here goes,

3 teams A, B and C.
1<=n<=5 the first 5 spots get points.
The points are 6-n, so (6-1) = 5, (6-2) = 4, and similarly 3,2 and 1.

Distribute these points among the 3 teams so that total does not exceed 6.

A 5
B 4, 1
C 3, 2

the least possible total/score is 5.

(I could be waaaay off)

5. For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3 since 75=3*5*5. How many two digit positive integers have length 6? Ans is 2 (what is the fastest way to do this?)

Q says the numbers are 2 digits so start with smallest prime number and multiply it 6 times, you will get 2*2*2*2*2*2 = 64
Now to get other number simply replace last 2 in above by next prime number ans is 2*2*2*2*2*3 = 96 this number is already close to 100 (which is 3 digit) so ans is 2

HarvardDreamin wrote:

camitava wrote:1. F:J = 3:5 and (F+40):J = 5:3 ---> Solve these two equs.

I tried that for the first one but didnt get 240..Do you mind showing your working if it works for you ? Thx

Hey after ur post, I also tried to solve the equs. But did not get the answer - 240. Is the OA correct? ORam I missing something?

Can someone please explain question 5 from the list?? Many Thanks.

Can someone please explain question 5 from the list which is
5. For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3 since 75=3*5*5. How many two digit positive integers have length 6? Ans is 2 (what is the fastest way to do this?) ??

Many Thanks.

Well, since length = 6, this means you have 6 prime numbers in your two-digit numbers. Now, let's start from the smallest on. The smallest two digit number to have n = 6 is 2^6 = 64, since 2 is the smallest prime number and you have 2 six times in 64. Now let's replace one of the 2's with a 3. You get a number which is equal to (2^5)*3 = 32*3 = 96. This is the second smallest two digit number to have n = 6, since 3 is immediately greater than 2. If you try to replace another 2 with a 3, you get a three digit number equal to (2^4)*(3^2) = 16*9 = 144.
So you have only 2 two-digit numbers with n, and those are 64 and 96.

Bschool08 wrote:Hello,

Can someone help me with these GMAT prep questions please? Thanks

1. The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the months of January is 3/5. If the fuel oil bill for February has been $40 more, the corresponding ratio would have been 5/3. How much was Alex's fuel oil bill for Jan? Ans is $240

I think this question is wrong. The ratio has to be 3/2 instead of 3/5...
Pl refer:
www.beatthegmat.com/gmat-prep-alex-ratio-t17390.html

Bschool08 wrote: 2. In the infinite sequence of (please note these are sub powers, the small text feature is not working) a1, a2, a3,.....an, each term after the first is equal to twice the previous term. If a5 - a3 = 12, what is the value of a1? Answer is 12/7

Bschool08,
are you sure the question is right...
because i find another question in which "a5 - a2 = 12" is used, an not "a5 - a3 = 12"

pl find the link:
https://www.beatthegmat.com/infinite-sequence-t2111.html