GRE Maths Questions

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Hia,

This being my first post here, I would like to give a short introduction. I am 24 and preparing for the GRE so that I can get into graduate school, I ultimately want a Phd in Artificial Intelligence. So to reach my goal, this GRE has to be taken, and taken soon. Maths is sure of high school level but sure is a lot trickier than meets the eye. I took the GRE once but bcoz of maths had to cancel scores. This time around, the preparations's gonna be intensive. I solved all the books I could get my hands on but there are a few questions I couldn't solve, or was doubtful bout them. I am posting them here and hope someone would lend a hand. The problem is that the source where I got the questions from doesn't have answers. So if you know how to solve them, Please be kind enough to tell me how. BTW the GRE gives you 45 minutes for 28 questions, so faster the solutions, the better. Well I guess, thats all the ado that's needed. Here are the questions:


1.Given A, B, C and D as four consecutive numbers,

6.jpg

if AD: AB = 9: 1 and AD: AC = 4:1, then what is the value of A, B, C and D?

A. -20, -16, -11, 16
B. -24, -20, 16, 36
C. -24, -4, 16, 36
& so on??

2. A number n when divided by 24 gives 21 as remainder. Which of the following can be the quotient?

A. 3
B. 4
C. 5
D. 6
E. 7

3. For the equation x^2- x- 2<or= 0; how many solutions are possible?
A. 1
B. 2
C. 3
D. 4
& so on?.

4. By weight liquid A makes up 7% of solution-I and 14.5% of solution-II. If 3 grams of solution-I is mixed with 2 grams of solution-II, then liquid A accounts for what percentage of weight of resulting solution?

5. If the sum of n different positive integers is less than 100, then what is the greatest possible value of n?

6. If the standard deviation of w + 6, x + 6, y + 6 is d, then is it greater than or less than r equal to the Standard Deviation of w, x, y

7. Given mode of a set as 70.
Col A: Mean of the set
Col B: 70


a. A greater
b. B greater
c. A and B equal
d. Answer cant be deducted from the data given.

8. Given a series a1, a2.......an. If a1 =4, a2 =-5 and an= a(n-1)+a(n-2), then
find the sum of first 100 numbers in the series?
[NOTE: 1, 2, (n- 2), (n-1) and n in the above question are subscripts].

...........................................................................................................

Please not that the questions CAN be wrong since the source isn't verifiable. Still these questions are important.

Here are my solutions, please correct if I am wrong.

1. No idea
2. All options are right
3. Infinite as x can be less than -1
4. 50%
5. 13
6. Same?
7. Option (d)
8. No Idea
 

RDV

2
0
Please see my responses labelled RDV

Hia,

This being my first post here, I would like to give a short introduction. I am 24 and preparing for the GRE so that I can get into graduate school, I ultimately want a Phd in Artificial Intelligence. So to reach my goal, this GRE has to be taken, and taken soon. Maths is sure of high school level but sure is a lot trickier than meets the eye. I took the GRE once but bcoz of maths had to cancel scores. This time around, the preparations's gonna be intensive. I solved all the books I could get my hands on but there are a few questions I couldn't solve, or was doubtful bout them. I am posting them here and hope someone would lend a hand. The problem is that the source where I got the questions from doesn't have answers. So if you know how to solve them, Please be kind enough to tell me how. BTW the GRE gives you 45 minutes for 28 questions, so faster the solutions, the better. Well I guess, thats all the ado that's needed. Here are the questions:


1.Given A, B, C and D as four consecutive numbers,

6.jpg

if AD: AB = 9: 1 and AD: AC = 4:1, then what is the value of A, B, C and D?

A. -20, -16, -11, 16
B. -24, -20, 16, 36
C. -24, -4, 16, 36
& so on??

[RDV: This should be done via cross checking the answers.. A is the answer]

2. A number n when divided by 24 gives 21 as remainder. Which of the following can be the quotient?

A. 3
B. 4
C. 5
D. 6
E. 7

3. For the equation x^2- x- 2<or= 0; how many solutions are possible?
A. 1
B. 2
C. 3
D. 4
& so on?.

[RDV: if x is said to be an integer, then 4 solutions are possible: -1,0,1 and 2. If any other integer is substituted for x, inequality would fail]

4. By weight liquid A makes up 7% of solution-I and 14.5% of solution-II. If 3 grams of solution-I is mixed with 2 grams of solution-II, then liquid A accounts for what percentage of weight of resulting solution?

[RDV: Let both Solution 1 and Solution 2 are 100 gms, hence A1=7 and A2=14.5
therefore, in 3gm solution: A1=3*7/100=.21 and A2=2*14.5/100=.29
hence, total A=.21+.29=.5
Total solution=5 gm
hence, A%=.5/5 *100=10%]

5. If the sum of n different positive integers is less than 100, then what is the greatest possible value of n?

6. If the standard deviation of w + 6, x + 6, y + 6 is d, then is it greater than or less than r equal to the Standard Deviation of w, x, y

7. Given mode of a set as 70.
Col A: Mean of the set
Col B: 70


a. A greater
b. B greater
c. A and B equal
d. Answer cant be deducted from the data given.

8. Given a series a1, a2.......an. If a1 =4, a2 =-5 and an= a(n-1)+a(n-2), then
find the sum of first 100 numbers in the series?
[NOTE: 1, 2, (n- 2), (n-1) and n in the above question are subscripts].

...........................................................................................................

Please not that the questions CAN be wrong since the source isn't verifiable. Still these questions are important.

Here are my solutions, please correct if I am wrong.

1. No idea
2. All options are right
3. Infinite as x can be less than -1
4. 50%
5. 13
6. Same?
7. Option (d)
8. No Idea
 

DavidSnider

Gold Member
477
124
5.
For this one just plug in the multiple choice into the formula
n(n+1)/2
 

RDV

2
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For Question 6: SD should be equal for both set of data.
For Question 7: You cannot find it from given data.
For Question 8: Well, this seems to be a different question, i guess answer options should help in zeroing out the answer.
Now to slove it:
a1= 4, a2=-5, a3=a1+a2, a4=a3+a2=a1+2*a2.. and so on..
so sum of n terms: a1 + (a1+a2)(1+1+2+3+5+8+13.....)
This is a fibonacci series.. there is no simple way of finding out the sum of this series.. but definitely.. the answer should be most negative value.
 
12
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For Question 6: SD should be equal for both set of data.
For Question 7: You cannot find it from given data.
For Question 8: Well, this seems to be a different question, i guess answer options should help in zeroing out the answer.
Now to slove it:
a1= 4, a2=-5, a3=a1+a2, a4=a3+a2=a1+2*a2.. and so on..
so sum of n terms: a1 + (a1+a2)(1+1+2+3+5+8+13.....)
This is a fibonacci series.. there is no simple way of finding out the sum of this series.. but definitely.. the answer should be most negative value.
Thanks a lot. You guys have been great. I mean I was struggling over these questions for so long, and you guys solved them in the blink of an eye, lol.

No Seriously, Thank you, a lot.

One doubt remains:

8. In the GRE the answers are close enough, e.g., choices can be as close as -10001 and -10002, -10003, In that case can you help how choose the answer?

And, as I keep doing questions, the doubts would keep coming, hope you guys won't mind If I chip in a few more everyday after the end of my study sessions,

Here are some more in the next post.

Thanks a lot once more, you pulled me out of my misery.
 
12
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12
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More questions:


9. Given N= v*w*x*y*z - (v+w+x+y+z). If N is an even integer, then how many of v, w, x, y, z will need to be even numbers?

My Ans: All

10. If |x|<or= 6; |y|<or= 4, then find the greatest possible value of |x/y|.

My Ans: 3/2

11. The probability of raining tomorrow is 0.49.
Col A: The probability that it will rain tomorrow and George eats the food
Col B: 0.54

My ans: .49 * .54= .2646


12. If twice the average of x, y and z, when divided by 7 gives remainder 1, then what is the remainder, when average x, y and z is divided by 7?

My ans: 2

13. What is the least common factor of 123 × 255
A. 3
B. 7
C. 17
& so on?.

My Ans: 3

14. Col A: 1/25+1/26+1/27+1/28+1/29+1/30
Col B: 0.2

a. A greater
b. B greater
c. A and B equal
d. Answer cant be deducted from the data given.

[This is a simple calculation but can can anyone tell me how to solve it in a minute or so? Some short cut method?]
 
105
0
for q14
0.2 = 6/30 = 1/30 + 1/30 + 1/30+1/30+1/30+1/30 < 1/25+1/26+1/27+1/28+1/29+1/30
so column A is greater

and for 10, what if x = 5 and y = 0.00000000000000000000001?


and for 9.

(1,3,5,7,9) none of the nubmers are even but N is even.
 
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12
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for q14
0.2 = 6/30 = 1/30 + 1/30 + 1/30+1/30+1/30+1/30 < 1/25+1/26+1/27+1/28+1/29+1/30
so column A is greater

and for 10, what if x = 5 and y = 0.00000000000000000000001?


and for 9.

(1,3,5,7,9) none of the nubmers are even but N is even.
Yes, all 3 seem correct. You are a GENIUS.
 
12
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Any help for the others??
 
12
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Maths People, answer to the wailing of a child lost amongst mindless puzzles....
 

uart

Science Advisor
2,776
9
Maths People, answer to the wailing of a child lost amongst mindless puzzles....
Question 8 is interesting.

The recurrence relation is the same as the Fibonacci series but the starting conditions are different. This series can be written as a linear combination of two Fibonacci series. In particular :

[tex] a_k = 4 F_k - 9 F_{k-1}\,\,\,\,\, : k \geq 1 [/tex].

Where [itex]F_k[/itex] is the kth term in the Fibonacci series.
BTW : The multiple of 4 is from the first term in the series and the multiple of -9 from 4 - 9= -5, the second term in the series.

The Fibonacci series has many interesting properties and one of them is that the sum of the first N terms of the series is exactly one less than the (N+2)th term (for example the sum of the first 5 terms is equal to the 7th term minus 1). The sum of the first 100 terms of our series can therefore be written as :

[tex]\sum_{k=1}^{100} a_k = 4 (F_{102} - 1) - 9 (F_{101} - 1)[/tex]

[tex]\sum_{k=1}^{100} a_k = 4 F_{102} - 9 F_{101} + 5[/tex]

Since this is the difference of two very large numbers it's probably worthwhile collapsing it a bit before evaluation. You can collapse this series from it's tail by using the recursion relation F_(k+2) = F_k + F_(k+1) a few times. For example if i apply that relation to the F_102 term in the above expression I get :

[tex]\sum_{k=1}^{100} a_k = 4 F_{100} - 5 F_{101} + 5[/tex]

And doing it once more, this time with the F_101 term I get :

[tex]\sum_{k=1}^{100} a_k = -F_{100} - 5 F_{99} + 5[/tex]

There's no point going any further as the coefficients will just get larger, this is a good point to stop as the two Fibonacci terms are both the same sign.

Finally you can express the Fibonacci terms (and hence the desired sum) in closed form using another interesting property of the Fibonacci series. That being :

[tex] F_k = \frac{1}{\sqrt{5}} \left( p^k - q^k \right)[/tex]

Where [itex]p = (1+\sqrt{5})/2 [/itex] and [tex]q = (1 -p)[/tex].

BTW. Numerically the sum comes out at approx [itex] -1.4488 \times 10^{21}[/itex]
 
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