from Internet resources, #20, 22,24,25 of section 13

isisalaska wrote:20- If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) s2 > 220
Answer= C

22- If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21
Answer= E
23- What is the value of t ?

(1) The average (arithmetic mean) of t2 and 8t is –8.
(2) sq. root of t^4=16
Answer= A



24- What is the area of a rectangular surface that has length x feet and width y feet ?

(1) y is the reciprocal of x.
(2) The perimeter of the rectangular surface is 5 feet.

How can you knwo with A only?

25- What is the greatest common divisor of positive integers m and n ?

(1) m is a prime number.
(2) m and n are consecutive integers.
Anser is B

1.)the sum of first n positive integers is given by n(n+1)/2....
the first statement says that S < 20... therefore the possible values of n is 1, 2, 3,4,5... the corresponding values of S are 1,3,6,10,15... so we dont get a defnite answer so insufficient

the second statement says that S^2 is > 220... this obviously is insufficient

now combining both we can see that only S=15 is the only possible answer
... so answer is C



2.) integer 42 has 8 factors they are 1,2,3,6,7,14,21,42... the only prime factor being 7

the first statement says that p>6.. so it culd be 7,14,21,42... so this insufficinet

the second statement says that p<21... so it culd be 1,2,3,6,7,14 ... so insufficient

combining both .. we get p culd be 7,14 ... so again insufficient ... so E


3.) the first statement says that ( t^2 + 8t )/2= -8... we get t^2 + 8t + 16 = 0 .... (t+4)^2 =0 .. so t = -4... so sufficinet

the second statement says that t^4 = 16 ... that gives t = + or - 2.. so not sufficient...


4.) area of rectangle = x*y..

the first statement says that y=1/x ... so area = x*y=x*1/x= 1 ... so A is sufficinet

the second statement says that 2(x+y)=5.. which is insufficient

5.) the q asks for the GCD of m & n ...

the first statement says that m is prime but says nothing abt n ... so insufficient

the second statement says that m and n are consecutive integers .. now any 2 consecutive integer are co prime that is they are prime to each other... that is the only factor common between them is 1 ... eg. 3 & 4, 12 & 13... so B is sufficient...

Gabriel, thank you for all your answers!!!

s is less than 20..But we do not know how many terms are a part of the sequence.

Sample this it could be 1,2,3 in which s = 6

It could be 1,2,3,4 ; s = 10

It could be 1,2,3,4,5 where s = 15

hence statement 1 alone is insufficient

Now Consider Statement II

s^2 is greater than 220. It could be 1,2,3,4,5,6 = 21 ; 21^2 = 441 which is greater than 220

It could be 1,2,3,4,5,6,7. = 28; 28^2 = 784

Hence Statement 2 alone is insufficient.

If you combine the two

S < 20 and S^2 < 220. Hence S can only be 15 i.e. sum of 1,2,3,4,5

Hence Answer Choice C

22- If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21

p is greater than 6. P can be 7 and P can be 14. Hence Statement I alone is insufficient

Now p < 21. Again p can be 6 or 7 or 14. Hence Statement II alone is insufficient

Now combine the two. the factor is greater than 6 but less than 21. Again it can be 7 or 14. Thus E


23- What is the value of t ?

(1) The average (arithmetic mean) of t2 and 8t is –8.
(2) sq. root of t^4=16

(t^2 + 8t) / 2 = -8

It's will become a quadratic equation wherein t^2 + 8t + 16 = 0

t^2 + 4t + 4t + 16 = 0

t (t + 4) + 4 (t +4) = 0

Thus the only solution is T = -4

Thus A alone is sufficient

Now consider Statement II

Square root of t^4 = 16

Thus t^2 = 16

The roots could be -4 and +4. Hence not sufficient

A alone is sufficient but B alone is not sufficient. Hence A

24- What is the area of a rectangular surface that has length x feet and width y feet ?

(1) y is the reciprocal of x.
(2) The perimeter of the rectangular surface is 5 feet.

Statement I : This tells us that y = 1/x or xy = 1. Thus area of the rectangle = 1 unit

Statement II : Tells us that 2x + 2y = 5 ; x + y = 2.5 ; Here x and y can have any arbitrary value. Thus II alone is insufficient.

It's A

25- What is the greatest common divisor of positive integers m and n ?

(1) m is a prime number.
(2) m and n are consecutive integers

Still working on this one!