[bhavin422]

Originally Posted by BizzareNym

guys, plz explain.


What is the value of integer x
1. x has exactly two factors
2. when x is divided by 2, the remainder is 0.

Thanks!

Ans C is perfectly acceptable ...
Conventionally , factors of a +ve no are +ve only ...
Its just like sq root of a no is always non negative or 0! = 1 ..

Also, if -ve factors for +ve nos were acceptable, then concept of prime nos also goes for a toss ...simple def of prime no is one which has only 2 factors, 1 and itself ..

So we say 5 is prime coz 1 and 5 are the only factors, and not -1 and -5, else every prime no would also hv 4 factors ...

Hence, St 1 : It is just any prime no ..not suff
St 2 : It is any even no ..not suff
Combined : it is even prime, hence 2 ...suff ..

Ans C

[deepakraam]

Solve this

Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of sqrt(x) every 10 minutes.Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

1) x = sqrt(y)
2) x > 8

[BizzareNym]

I thought the definition os prime is a positive integer which has only 2 factors.

Plus we are not cinsidering -ve factors of a positivie number. What we are considering is +ve factors( as factors as always meant to be +ve) of negative number.

Then I am right to say that -2 has two factors: 1,2.

And if I am right, then not C but E will be the answer. Plz feel free to object.

Originally Posted by bhavin422

Ans C is perfectly acceptable ...
Conventionally , factors of a +ve no are +ve only ...
Its just like sq root of a no is always non negative or 0! = 1 ..

Also, if -ve factors for +ve nos were acceptable, then concept of prime nos also goes for a toss ...simple def of prime no is one which has only 2 factors, 1 and itself ..

So we say 5 is prime coz 1 and 5 are the only factors, and not -1 and -5, else every prime no would also hv 4 factors ...

Hence, St 1 : It is just any prime no ..not suff
St 2 : It is any even no ..not suff
Combined : it is even prime, hence 2 ...suff ..

Ans C

[deepakraam]

Hi Bizzare,
The factors of -2 will be either -1,2 or 1,-2 .It won't be 1,2

[bhavin422]

Originally Posted by BizzareNym

guys, plz explain.

How many factors does -2 have?

In the light of above question, plz solve the below.

What is the value of integer x
1. x has exactly two factors
2. when x is divided by 2, the remainder is 0.

Thanks!

Originally Posted by BizzareNym

I thought the definition os prime is a positive integer which has only 2 factors.

Plus we are not cinsidering -ve factors of a positivie number. What we are considering is +ve factors( as factors as always meant to be +ve) of negative number.

Then I am right to say that -2 has two factors: 1,2.

And if I am right, then not C but E will be the answer. Plz feel free to object.

Interesting discussion ...
Yes, i concur with u for def of prime ...

And if we discuss prime factors of -ve nos, then by fundamental theorem of arithmetic , every integer greater than 1 can be expressed as unique product of prime nos ...
Fundamental theorem of arithmetic - Wikipedia, the free encyclopedia

So, again prime factorization is conventionally restricted to finding factors of +ve integers only ...

So, in St 1, x has exactly 2 factors indirectly tells u that that x is + ve and prime only, So i guess discussion of factors of -ve nos does not arise ...

[BizzareNym]

Bhavin/Deepak,

I am not convinced. A factor F of a number N is an integer which could divide the number N evenly into F equal parts. We can not have negative number of parts!
In short, as per my understanding, a factor is always positive.

Anyways, I think this dicsussion is getting too "mathemetical"
For now I reconcile myself with MGMat's explanation.

Thanks buddy!

Originally Posted by deepakraam

Hi Bizzare,
The factors of -2 will be either -1,2 or 1,-2 .It won't be 1,2

[BizzareNym]

I think it should be C.

After 60 mins, speed of x is x^4
speed of y is 64y

Question is whether x^4 > 64y

Stmnt 1: x = sqrt(y) => x^4 = y^2
Rephrasing the question: is y^2 >64y
Solving this equality we get
y^2 <= 64y for y <=64 --I
y^2 > 64y for y >64 --II

Two ranges of outcome. Not Suff

Stmnt 2: x >8
we cannot determine whether x^4 > 64y because we dont know about y. hence insuff

Combining 1 & 2:
since x>8 and y = x^2 leads to y >64

From II above, we know that y^2 > 64y for y>64. Hence sifficient.

Waiting for the OA.

Originally Posted by deepakraam

Solve this

Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of sqrt(x) every 10 minutes.Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

1) x = sqrt(y)
2) x > 8

[@nee!]

Solve this

Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of sqrt(x) every 10 minutes.Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

1) x = sqrt(y)
2) x > 8

end of hour

Speed of M 1 --> x^4
Speed of M 2 --> 64*y

option 1) then m1--> x^4 ,.....m2 --> 64*x*x
option 2) x > 8

combine both

x*x >64 so , Speed of m1 > Speed of m2
answer is : with both the options u cn solve

[pj02]

One more: Sorry if this is repost.

if x^2 + 5y = 49, is y an integer?
(1) 1 < x < 4
(2) x^2 is an integer.

[Darth Maul]

Originally Posted by pj02

One more: Sorry if this is repost.

if x^2 + 5y = 49, is y an integer?
(1) 1 < x < 4
(2) x^2 is an integer.

Will go with C

1) x can be fractions ...not suff
2) x^2 = set of all integers .... not suff

1 & 2 )

x can be 2 or 3

when x = 2
y = 9

when x = 3
y = 8

combining 1 & 2 is sufficient