Difficult Math Question #22 - Rates

[800guy]

OA coming after some people have tried to answer... see the attachment to view problem.

[gamemaster]

All they ask is weather:

x^4 > 2^6 * y

[abby_g]

I hope i can explain it:

From the given data:
LHS: x ( sqrt x ) ^6 = x^4
RHS: 2^6 * y
the equation is x^4 = y* 2^6

so what is asked is whether y > 2^6?

Condition 1:
x= sqrt y
:arrow: x^4 = y^2 which may or may not be greater than y * 2^6 unless
y> 2^6, which we cannot deduce here.

Contition 2:
x>8 . Now lets put x = 8 in our equation
:arrow: 8^4 = y * 2^6
:arrow: (2^3)^4 = y * 2^6
:arrow: (2^6 ) * (2^6) = y * 2^6
:arrow: y = 2^6. now since x> 8 so y > 2^6 . it satisfies.

I suppose the answer is B. THank you.

[800guy]

OA--see the attachments

[anandsebastin]

A

After 1 hr, speed of missile A = x^4
missile B = y^7
Q: Is x^4>y^7?

Statement 1:
x = sqrt(y)
x^4 = (sqrt(y))^8

But, at 1 hr, speed of B = y^7 SUFF

Statement 2:
INSUFF without value for y

[kulksnikhil]

I hope i can explain it:

From the given data:
LHS: x ( sqrt x ) ^6 = x^4
RHS: 2^6 * y
the equation is x^4 = y* 2^6

so what is asked is whether y > 2^6?

Condition 1:
x= sqrt y
:arrow: x^4 = y^2 which may or may not be greater than y * 2^6 unless
y> 2^6, which we cannot deduce here.

Contition 2:
x>8 . Now lets put x = 8 in our equation
:arrow: 8^4 = y * 2^6
:arrow: (2^3)^4 = y * 2^6
:arrow: (2^6 ) * (2^6) = y * 2^6
:arrow: y = 2^6. now since x> 8 so y > 2^6 . it satisfies.

I suppose the answer is B. THank you.

Post1:
I agree with this answer... Answer is B ?


Post2:
For a moment let us consider B is correct. Had we come to a conclusion that Missile 1 is NOT going faster than Missile 2, our answer to the question "Is Missile 1 travelling faster than Missile 2" would have been 'NO'. But we would have arrived at the answer (as NO) using 2 alone without the help of 1... then should be answer as B or E (because, the answer is NO)

[Bharadwaj]

Missile-I squares its speed in 20 mins where as Missile-II doubles its speed in 10 mins. So all we need is the relation between the speeds of Missile-I and Missile-II, which we can find in stmt-1.

So answer is A.

[Bharadwaj]

I hope i can explain it:

From the given data:
LHS: x ( sqrt x ) ^6 = x^4
RHS: 2^6 * y
the equation is x^4 = y* 2^6

so what is asked is whether y > 2^6?

Condition 1:
x= sqrt y
:arrow: x^4 = y^2 which may or may not be greater than y * 2^6 unless
y> 2^6, which we cannot deduce here.

Contition 2:
x>8 . Now lets put x = 8 in our equation
:arrow: 8^4 = y * 2^6
:arrow: (2^3)^4 = y * 2^6
:arrow: (2^6 ) * (2^6) = y * 2^6
:arrow: y = 2^6. now since x> 8 so y > 2^6 . it satisfies.

I suppose the answer is B. THank you.

If you are using the equation you deduced using stmt-1 in stmt-2, then answer hast to be C(if you can arrive at a single answer) else it must be E. It can not be B.

[Bharadwaj]

I hope i can explain it:

From the given data:
LHS: x ( sqrt x ) ^6 = x^4
RHS: 2^6 * y
the equation is x^4 = y* 2^6

so what is asked is whether y > 2^6?

Condition 1:
x= sqrt y
:arrow: x^4 = y^2 which may or may not be greater than y * 2^6 unless
y> 2^6, which we cannot deduce here.

Contition 2:
x>8 . Now lets put x = 8 in our equation
:arrow: 8^4 = y * 2^6
:arrow: (2^3)^4 = y * 2^6
:arrow: (2^6 ) * (2^6) = y * 2^6
:arrow: y = 2^6. now since x> 8 so y > 2^6 . it satisfies.

I suppose the answer is B. THank you.

If you are using the equation you deduced using stmt-1 in stmt-2, then answer hast to be C(if you can arrive at a single answer) else it must be E. It can not be B.

[shobhits]

The question asks: Is x^4 > (2^6)y?
Statement 1: x= y^.5
--------------------
If y = 4, then x = 2
x^4 = 2^4 = 16
(2^6)y = 64 x 4 = 256
Therefore, Is x^4 > (2^6)y? No

If y = 100, then x = 10
x^4 = 10^4 = 10000
(2^6)y = 64 x 100 = 6400
Therefore, Is x^4 > (2^6)y? Yes

Statement 1 is NOT sufficient.

Statement 2: x > 8
------------------
If x = 9

x^4 = 9^4 = 6561

6561/64 ~ 6400/64 = 100

We can't say if y is less than or greater than 100. Hence, NOT sufficient.

But if we combine, Statement 1 and 2:
-------------------------------------
we get x= y^.5 and x > 8
If x = 8, then x^4 = 8^4 = 4096 and (2^6)y = (2^6) x 64 = 4096 i.e., x^4 = (2^6)y, when x = 8. For any value of x > 8, the inequality x^4 > (2^6)y is always TRUE.

Therefore, the answer is C

[diebeatsthegmat]

OA coming after some people have tried to answer... see the attachment to view problem.

answer should be C
after an hour x will increase x^4
after an hour y will increase 64 y
now we have to decide if x^4>64
1/ x=sqtr y so x^4=y^2
>>> now we have to decide if y^2>64y <=> y>64? we dont know the value of y so insufficient.
2/ x>8 clearly insufficient because we dont know anything about y
1+2
x>8 or squrt y>8 or Y>64 sufficient
C