If x and y are non-zero integers and x + |y = 32, what is xy?
(1) -4x 12y = 0
(2) x| |y = 16
[QUOTE=rohitforever = 32 this is a rhombus with 4 vertices (-32,0) (0,-32) ( 32,0) & (0,32) or it can be displayed with the delp of 4 eqns
x+y=32 x-y=32 y-x=32 x+y=-32
1=> y=-1/3 x this is a straight line with negative slope hence it passes through x-y=32 & y-x=32 on solving we get two points (24,- &(8,-24) so NOT SUFF
2=> this is the curve inthe form of > 1&2=> putting the points (24,- & (8,-24) in x-|y=16 both satisfies so NOT SUFF So ans is E IMO Rohit, Actually statement 1 is sufficient.
1. -4x 12y = 0 -4x = 12y So...x=-3y
Now as we know x and y are non-zero integers, This tells us X and Y have different signs. ( -,+)
we can also say x| = 3|y
Using this and x| + |y = 32,
We can find that x| = 24 an |y = 8
Still we don't know which one is negative and which one is positive but since we know that they have different signs... we can say xy= - 192
Hence statement 1 is SUFFICIENT
Now : (2) x| - |y = 16
Also we know that x| + |y = 32, we can find that x| = 24 an y = 8
But we dont know their signs and we cant get any idea about that so xy can be either - 192 or +192
1) either p is -ve and q is +ve or p is +ve and q is -ve ..
r can be both ... Not Suff
2) either p is -ve and r is +ve or p is +ve and r is -ve .. q can be both ... Not Suff
1&2)
if p is +ve ... q and r are -ve qr is +ve ..pqr is +ve
if p is -ve ...q and r are +ve qr is +ve ..pqr is -ve
Hence not suff
Though Ans should be E, your reasoning is incorrect .. Statement in bold is incorrect ... P It is E ...coz combined, p is -ve and q & r are +ve, however qr 1 ...hence insuff ..
If x and y are non-zero integers and x + |y = 32, what is xy?
(1) -4x 12y = 0
(2) x| |y = 16
[QUOTE=rohitforever = 32 this is a rhombus with 4 vertices (-32,0) (0,-32) ( 32,0) & (0,32) or it can be displayed with the delp of 4 eqns
x+y=32 x-y=32 y-x=32 x+y=-32
1=> y=-1/3 x this is a straight line with negative slope hence it passes through x-y=32 & y-x=32 on solving we get two points (24,- &(8,-24) so NOT SUFF
2=> this is the curve inthe form of > 1&2=> putting the points (24,- & (8,-24) in x-y=16 both satisfies so NOT SUFF So ans is E IMO
Rohit, Actually statement 1 is sufficient.
1. -4x 12y = 0 -4x = 12y So...x=-3y
Now as we know x and y are non-zero integers, This tells us X and Y have different signs. ( -,+)
we can also say x = 3|y
Using this and x| + |y = 32,
We can find that x| = 24 an |y = 8
Still we don't know which one is negative and which one is positive but since we know that they have different signs... we can say xy= - 192
Hence statement 1 is SUFFICIENT
Now : (2) x| - |y = 16
Also we know that x| + |y = 32, we can find that x| = 24 an y = 8
But we dont know their signs and we cant get any idea about that so xy can be either - 192 or +192
Well.. this problem confused me. By definition , a factor a positive integer which could divide a number evenly. Thus, according to me, -2 has only two factors : 1,2
Given that, the ans should be E.
But the DS problem that I posted here is in Manhattan Number Properties book, Chpater 10, Page 117 which says answer is C
I dont agree to this answer though.
the answer must be option E
-2 is divisible by 1 and 2 to give you integer output, hence 2 factors.. hope that helps ;)
For the below q
What is the value of integer x
1. x has exactly two factors ---> All prime nos 2. when x is divided by 2, the remainder is 0.-----> All even nos
Combining both the statements we get even prime which is 2. I feel combining both the statements we can say that x is 2
factors of -2 are 2, -2, 1, -1
1) all primes .. not suff 2) all even numbers..
1&2) 2
Hence C
whats the OA ?
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.
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 ..
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?
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.
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 ..
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!
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 ...
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 ...
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!
Hi Bizzare, The factors of -2 will be either -1,2 or 1,-2 .It won't be 1,2
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 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.
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?
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 😐
&(8,-24) so NOT SUFF