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
from Internet resources, #20, 22,24,25 of section 13
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1.)the sum of first n positive integers is given by n(n+1)/2....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
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...
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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!
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!