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 ≠ 0, then √(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⁄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
GMATPrep Tough Questions
3) IMO D... Since 0<n<200 and 7n/30 (simplified)...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 ≠ 0, then √(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⁄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
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 ≠ 0, then √(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⁄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
a. > 2
b. between 1 and 2
c. between ½ and 1
d. between ¼ and ½
e. < ¼
Ans. C
2) If x ≠ 0, then √(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⁄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
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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 ≠ 0, then √(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
Answer E: Its very simple since √(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 √(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⁄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
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 ≠ 0, then √(x^2)/x =
a. -1
b. 0
c. 1
d. x
e. |x|/x
Answer E: Its very simple since √(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 √(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⁄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
What if K is negative ??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.
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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.Pranay wrote:What if K is negative ??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.
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.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 ≠ 0, then √(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⁄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
Sorry read the question wrong! IMO B with prime factors 2, 3 & 5.apple100 wrote:3) IMO D... Since 0<n<200 and 7n/30 (simplified)...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 ≠ 0, then √(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⁄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
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.
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. 2π
b. 9π⁄4
c. 7π⁄2
d. 9π⁄2
e. 3π
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. 2π
b. 9π⁄4
c. 7π⁄2
d. 9π⁄2
e. 3π
Last edited by varunkh70 on Thu Jun 11, 2009 3:49 pm, edited 3 times in total.
- ssmiles08
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IMO Bvarunkh70 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
[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
- ssmiles08
- Master | Next Rank: 500 Posts
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r---> directly proportional to a^2varunkh70 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---> 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
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
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- Master | Next Rank: 500 Posts
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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)/bssmiles08 wrote:r---> directly proportional to a^2varunkh70 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---> 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)
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
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
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- 7117821-GMAT-Quant-Useful.pdf
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