Problem Solving

Hello All,

Could we have this post as a repository for tough(700 level) Gmat Prep Quant PS questions? I think this could be made into a sticky post so that BTG members can have a good question bank at hand! To start with I have doubts with the following questions which have been obtained from GMATPrep Software after repeated testing. I request you to provide solutions to these answers.

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8


OA will be provided later!

~Varun

varunkh70 wrote:Hello All,

Could we have this post as a repository for tough(700 level) Gmat Prep Quant PS questions? I think this could be made into a sticky post so that BTG members can have a good question bank at hand! To start with I have doubts with the following questions which have been obtained from GMATPrep Software after repeated testing. I request you to provide solutions to these answers.

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8


OA will be provided later!

~Varun

3) IMO D... Since 0<n<200 and 7n/30 (simplified)...
n must be multiples of 30 since 5 and 6 (when multipled equal 30) cannot be divide into 7... So n can be 30,60,90,120, 150, 180.

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼
Ans. C

2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
Ans. E

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

My Ans. Agree with the working of Apple.

Will post explanation, if the answers are correct!

Pranay

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

Answer: D

Explanation:
lets substitute k= 1,2,3 and 4
that gives us the value of the expression as 1/2, -1/4, 1/8, -1/16 and so we now know the pattern. Since T is summation of the first 10 terms lets just add the firts two which gives us 1/4. Now as we see 1/8 is greater than 1/16 therefore all future terms will add something positive to 1/4 however since the fraction goes on incresing later terms will be negligible and definitely not greater than 1/4 so our term T will be a little greater than 1/4 but less than 1/2. Hence answer is D.


2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x

Answer E: Its very simple since &#8730;(x^2) can either be negative or positive we put it as |x| and that divided by x will result in choice E. Even by pluggin in if x=2 , then &#8730;(x^2 could be +2 or -2 and that will give amiguous ans either -1 or 1 and if x=0 then the answer will be zero. E is the only option that satisfies all these.

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

Answer B

14N/60 = 7n/30. Since 30 is a factor it can be broken down to the following prime factors. 2x3x5. Now other prime factors are 7,11,13 etc however we can say for sure that 2,3,and 5 are definite factors of n but not 7 since 7n is divisible by 30. and since its divisible by 30 n cant be a multiple of 11,13 as it has to be less than 200. So we have 3 positive prime factors. 2,3 and 5

Naruto wrote:1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

Answer: D

Explanation:
lets substitute k= 1,2,3 and 4
that gives us the value of the expression as 1/2, -1/4, 1/8, -1/16 and so we now know the pattern. Since T is summation of the first 10 terms lets just add the firts two which gives us 1/4. Now as we see 1/8 is greater than 1/16 therefore all future terms will add something positive to 1/4 however since the fraction goes on incresing later terms will be negligible and definitely not greater than 1/4 so our term T will be a little greater than 1/4 but less than 1/2. Hence answer is D.

What if K is negative ??

Pranay wrote:

Naruto wrote:1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

Answer: D

Explanation:
lets substitute k= 1,2,3 and 4
that gives us the value of the expression as 1/2, -1/4, 1/8, -1/16 and so we now know the pattern. Since T is summation of the first 10 terms lets just add the firts two which gives us 1/4. Now as we see 1/8 is greater than 1/16 therefore all future terms will add something positive to 1/4 however since the fraction goes on incresing later terms will be negligible and definitely not greater than 1/4 so our term T will be a little greater than 1/4 but less than 1/2. Hence answer is D.

What if K is negative ??

Well pranay its a good doubt in that case the answer would be a however i dont think varun has posted the question properly, as u can read it mentions T is sum of first 10 k and not the expression, wouldnt that make the whole presumption wrong, so similarly i feel he forgot to mention that k is a positive integer, otherwise we can always put in other doubts like what if k is a fraction...etc. Lets wait for the OA.

varunkh70 wrote:Hello All,

Could we have this post as a repository for tough(700 level) Gmat Prep Quant PS questions? I think this could be made into a sticky post so that BTG members can have a good question bank at hand! To start with I have doubts with the following questions which have been obtained from GMATPrep Software after repeated testing. I request you to provide solutions to these answers.

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8


OA will be provided later!

~Varun

3. The only only intergers less than 200 for which 14N/60 is an integer are 60 120 180. All these have only powers of 2, 3, 5 as prime factors. Hence B.

apple100 wrote:

varunkh70 wrote:Hello All,

Could we have this post as a repository for tough(700 level) Gmat Prep Quant PS questions? I think this could be made into a sticky post so that BTG members can have a good question bank at hand! To start with I have doubts with the following questions which have been obtained from GMATPrep Software after repeated testing. I request you to provide solutions to these answers.

1) (-1^(k+1)).(½^k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼

2) If x &#8800; 0, then &#8730;(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x

3) If n is a positive integer less than 200 and 14n&#8260;60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8


OA will be provided later!

~Varun

3) IMO D... Since 0<n<200 and 7n/30 (simplified)...
n must be multiples of 30 since 5 and 6 (when multipled equal 30) cannot be divide into 7... So n can be 30,60,90,120, 150, 180.

Sorry read the question wrong! IMO B with prime factors 2, 3 & 5.

Thanks to everyone for their help. Here are the OAs :

1) D
2) E
3) B

Good Explanations I must say!

Here are more questions from Gmatprep(Please do try to provide the working) :

1)10^8 – 10^2 / 10^7 – 10^3 is closest to which of the following?
a. 1
b. 10
c. 10^2
d. 10^3
e. 10^4

2)The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase

3)PQ is parallel to OR. OR = 18. What is the length of minor arc PQ(I can't understand the question )
a. 2&#960;
b. 9&#960;&#8260;4
c. 7&#960;&#8260;2
d. 9&#960;&#8260;2
e. 3&#960;

varunkh70 wrote:
14) 10^8 – 10^2 / 10^7 – 10^3 is closest to which of the following?
a. 1
b. 10
c. 10^2
d. 10^3
e. 10^4

IMO B

[10^2*(10^6 -1)] / [10^3*(10^4 -1)]

(10^6 -1)~10^6 (subtracting 1 is trivial); same goes for (10^4 -1) ~ 10^4

10^2/10 = 10

Yes right! the Minus 1 can be neglected...My Bad.. OA is B

varunkh70 wrote: 2)The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase

r---> directly proportional to a^2
r---> inversely proportional to b

b now becomes 2b
which means r become r/2.
if r becomes r/2 ----> a^2 becomes a^2/4 [(a/2)*(a/2)]
to change r/2 back to r; we have to multiply (a^2/4)*4

so we are increasing a 40% for r to remain the same.

IMO (D)

Hi All,

Can anyone please help me with the 2 out of the 3 new questions? I need a deeper explanation for the 2nd and 3rd questions(the second set). Can the instructors please let me know how to be really quick at these problem types?

Thanks,
Varun

ssmiles08 wrote:

varunkh70 wrote: 2)The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?
a. 100% decrease
b. 50% decrease
c. 40% decrease
d. 40% increase
e. 50% increase

r---> directly proportional to a^2
r---> inversely proportional to b

b now becomes 2b
which means r become r/2.
if r becomes r/2 ----> a^2 becomes a^2/4 [(a/2)*(a/2)]
to change r/2 back to r; we have to multiply (a^2/4)*4

so we are increasing a 40% for r to remain the same.

IMO (D)

This was a really good explanation, however Varun am not sure but u might find mine a little more easy to get, we know that r=(a^2)/b
lets assume r=1/2, now here a=1 and b=2. if b increases by 100% so it becomes 4, now to maintain r=1/2, a^2=2, therefore a= root 2=1.41, so a has increased by approx 41%, hence D.

Hi All,

I got this pdf from "I just beat the gmat!" section. It was shared by agoyal2 who got a score of 730 (phew!). I am attaching the same here.

Thanks,
syr