GMAT Problem Solving Discussions

MBA
2801
Q How many numbers beloe 200 have exactly 6 devisors?



6 =1*6 or 2*3

Hence, No must be of the form N= a^5 or a^2*b or a*b^2 where a and b are prime ..

a^5 : only 1 poss i.e 2^5 ....total 1 no

a^2*b types below 200 :

2 and prime below 50 i.e 3,5,7,11,13,17,19,23,29,31,37,41,43,47 i.e14 nos
3 and prime below 22 i.e 2,5,7,11,13,17,19 i.e 7 nos
5 and prime below 8 i.e 2,3,7 i,e 3 nos
7 and prime below 4 i.e 2,3 i.e 2 nos

Hence, total 27 nos below 200 have exactly 6 divisors .

Pls let me know if i have missed out a few nos ..

Also brief us, if smbdy aware of a shorter method !
2802
Is the ans for the above q is option B)7

the nos will 10!
10!+1
10!+2.......10!+20

and the nos divisible will be
10!
10!+3
10!+6......10!+18

So total no of nos is 7


Gr8 Approach deepak (Y)
actually the worst thing is , I don't know the answer but i think i might have just solved it ........ i don't even know if it is right as well so guys please help me.......


Question :- How many integers are divisible by 3 between 10! and 10!+20 inclusive?????

A. 6
B. 7
C. 8
D. 9
E. 10

10! =3628800
10!+20= 3628820

we have to find the integers that are divisble by 3 from 3628800 to 3628820.... obviously ,3628800, 3628803 ,3628806,3628809,3628812,3628815,3628818....one way to consider it easy is the numbers are from 00-20 ...and only 6 digits are divisble by 3 . but as they INCLUSIVE so we have to add 3628800 and 3628820 and only 3628800 is divisble by 3.

I hope the Answer is (7)

@Deepak..... you rmethod is so easy , I had to find the 10! first and then do the addition...... could u please helpme explaining more about how u did the question ??? Thanks !
2803

Puys.. plz elaborate..

Should be 2^2 * 5 * 13 = 260 ..

2804
extra time=1 hour
extra distance=70 miles
so speed=70
this speed is 5 more than normal so normal speed=70-5=65

so for two hours and 10 miles faster,distance=2*(65+10)=2*75=150

Well even I started with the same same approach but later I realized that:
1) Extra distance 70 miles is not being covered only in the last 1 hour but in the entire journey.
2) And the speed was 5 mph greater not only in the last hour but in the entire journey.

I guess its just the coincidence that answer comes out to be the same only for this particular values. I would rather suggest ppl to follow Vyombs method.
Puys what do u think about this approach???
plz correct me if I am wrong....
2805
Gr8 Approach deepak (Y)
actually the worst thing is , I don't know the answer but i think i might have just solved it ........ i don't even know if it is right as well so guys please help me.......


Question :- How many integers are divisible by 3 between 10! and 10!+20 inclusive?????

A. 6
B. 7
C. 8
D. 9
E. 10

10! =3628800
10!+20= 3628820

we have to find the integers that are divisble by 3 from 3628800 to 3628820.... obviously ,3628800, 3628803 ,3628806,3628809,3628812,3628815,3628818....one way to consider it easy is the numbers are from 00-20 ...and only 6 digits are divisble by 3 . but as they INCLUSIVE so we have to add 3628800 and 3628820 and only 3628800 is divisble by 3.

I hope the Answer is (7)

@Deepak..... you rmethod is so easy , I had to find the 10! first and then do the addition...... could u please helpme explaining more about how u did the question ??? Thanks !


You don't need to calculate the value of 10!.10! = 1*2*3....*10.So 10! is divisible by 3.Rest of the sum I did in the same way as u did.

-Deepak.
2806
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A) 1 / R+2
B) 1/(2R+2)
C) 1/(3R+2)
D) 1/(R+3)
E) 1/(2R+3)
2807
Q How many numbers beloe 200 have exactly 6 devisors?

Q A number has got only 12 factors and it consist of 3 prime factors. the sum of these prime factors is 20, find the minimum possible number??



here is the answer for B) 260..

The approach for first is exactly the same:

(5+1) * 1
(2+1) * (3+1)

so start with the 2 and keep on multiplying unless less you keep the number below 200
2808
here is the answer for B) 260..

The approach for first is exactly the same:

(5+1) * 1
(2+1) * (3+1)

so start with the 2 and keep on multiplying unless less you keep the number below 200

can you please elaborate your approach 😉
thanks in advance

Regards,
Varun V.
2809
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A) 1 / R+2
B) 1/(2R+2)
C) 1/(3R+2)
D) 1/(R+3)
E) 1/(2R+3)



My take on the above q is option E)1/(2R+3)
2810
Guys... i know this is a reply to old post... but i was not able to solve this and the guy who solved this ,I couldnt understand his analysis...

Can anyone throw some light on this problem?
Fundoo problem
-------------------

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
2811
This one was also not discussed. I dont know the answer.
Here is one more......

In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?

A) 24
B) 52
C) 96
D) 144
E) 648
2812
deepakraam Says
My take on the above q is option E)1/(2R+3)



Big Q is HOWWWWWWWWWWWWWW?????

i could not mak ethe equations...
2813
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A) 1 / R+2
B) 1/(2R+2)
C) 1/(3R+2)
D) 1/(R+3)
E) 1/(2R+3)



Let Henry's Income be - n
If he saves - s
He'll spend - (n-s)

Next yr ->
For every 1 $ - $ to spend
So, for s $ - ?

= s which is equal to 1/2(n-s) {half he spends this yr}

We need to find what fraction of his income shd he save this yr..
i.e s/n = ??

Solving -

s = 1/2
2 = /s
2+2r = n/s - 1

2r+3 = n/s

s/n = 1/


IMO - E
2814

Hey guys,

This may not be the most appropriate place to raise the question but I am posting it here for max visibility.

I have taken 3 kaplan tests so far and developed a feeling that the Quant is easier than actual GMAT. Before I become complacent with my prep, i would like to know how others feel about kaplan quant.

As for kaplan verbal, i find some problems distorted and their reasoning even more annoying. They are not as clear as OG's problems, and for that matter MGmat too.

Curious to know your opinion.

Thanks!!

2815
Originally Posted by nairpraveenk
Fundoo problem
-------------------

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


I think it's E..

wats the OA?
2816
Guys... i know this is a reply to old post... but i was not able to solve this and the guy who solved this ,I couldnt understand his analysis...

Can anyone throw some light on this problem?

Originally Posted by nairpraveenk
Here is one more......

In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?

A) 24
B) 52
C) 96
D) 144
E) 648



Nice one!!

IMO - 'B'

wats the OA??
I can explain if the answer's right!
2817

does the question say both 10! and 10! + 20 inclusive? if not then the ans will be 6. whats the OA btw?

Is the ans for the above q is option B)7

the nos will 10!
10!+1
10!+2.......10!+20

and the nos divisible will be
10!
10!+3
10!+6......10!+18

So total no of nos is 7
2818

sorry, couldn't locate the original post therefore picking from here.
I think the ans should be A. waiting for the OA before I post explanation.

I think it's E..

wats the OA?


Quote:
Originally Posted by nairpraveenk
Fundoo problem
-------------------

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
2819
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
A) 1 / R+2
B) 1/(2R+2)
C) 1/(3R+2)
D) 1/(R+3)
E) 1/(2R+3)


My take is C
Waiting for OA
2820

Determine in what ratio must water be mixed with milk so as to gain 30% by selling this mixture at cost price?
a.3:10
b.1:3
c.3:5
d.2:3
need help..