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

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

Tue Mar 27, 2007 8:11 am
20- If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) s2 > 220

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

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

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

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Cybermusings Legendary Member
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Wed Mar 28, 2007 4:44 am
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

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!

Joined
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Tue Mar 27, 2007 10:05 am

_________________

Cybermusings Legendary Member
Joined
27 Mar 2007
Posted:
559 messages
Followed by:
2 members
5
Wed Mar 28, 2007 4:44 am
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

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!

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