If Fran jumps straight up off the floor and lands on her fee

Question

If Fran jumps straight up off the floor and lands on her feet T seconds later, her feet will reach a maximum height of 1.22T^2 meters above the floor. On one such jump, was Fran off the floor for less than 1 second?

(1) On her jump Fran’s feet reached a maximum height of 1 meter above the floor

(2) On her jump Fran spent more than 1/4 second ascending

Bunuel · Accepted Answer

If Fran jumps straight up off the floor and lands on her feet T seconds later, her feet will reach a maximum height of 1.22T^2 meters above the floor. On one such jump, was Fran off the floor for less than 1 second?

(1) On her jump Fran’s feet reached a maximum height of 1 meter above the floor --> 1.22T^2 = 1 --> we can find T and answer whether it's less than 1. Sufficient.

(2) On her jump Fran spent more than 1/4 second ascending --> if she spent 1/3 second ascending, then the answer is YES but if she spent 100 seconds ascending, then the answer is NO. Not sufficient.

Answer: A.

gmatkum · Answer

1 - sufficient. 1.22T^2 = 1, we can solve for T and hence know if it is > 1 or
< 1

2 - insufficient. If the ascend is 1/3sec, then the total is 2/3 sec which is < 1.
If the ascend is 1 sec, then total = 2 sec which is > 1

I'd vote for A

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If Fran jumps straight up off the floor and lands on her feet T seconds later, her feet will reach a maximum height of 1.22T^2 meters above the floor. On one such jump, was Fran off the floor for less than 1 second?

(1) On her jump Fran’s feet reached a maximum height of 1 meter above the floor

(2) On her jump Fran spent more than 1/4 second ascending

Modify the original condition and the question. Since her feet will reach a maximum height of 1.22t^2 after t seconds later, you need to figure out t. So, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), you can find out value of t from 1.22t^2=1, which is sufficient.
For 2), 1/4 second was spent more. So, if it is 1.1/4 seconds, it is yes. If it is 1 second, it is no and not sufficient. Therefore, the answer is A.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

GDT · Answer

VeritasKarishma

can you pls explain me how we analysed statement 2

KarishmaB · Answer

Time of jump = T sec
Height = 1.22*T^2

So more the time, more the height. If time of the jump is 1 sec, height of the jump is 1.22 m and so on. If height of jump is less than 1.22 m, time of jump is less than 1 sec. If height of jump is more than 1.22 m, time of jump is more than 1 sec.

(1) On her jump Fran’s feet reached a maximum height of 1 meter above the floor

Since height of jump is less than 1.22 m, the time of jump must have been less than 1 sec. Sufficient.

(2) On her jump Fran spent more than 1/4 second ascending

We know that she spent more than 1/4 sec ascending. 
She could have spent .3 sec ascending and .3 sec descending (or 0.2 secs descending we don't know) so her overall time could have been less than 1 sec.
Or she could have spent 2 secs ascending and some time descending but her overall time will definitely be more than 1 sec here.

Answer (A)

dungltp9 · Answer

Can someone please explain clearly the meaning of "On her jump Fran spent more than 1/4 second ascending"? After reading answers from experts I still don't get it.

Thank you!

bumpbot · Answer

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If Fran jumps straight up off the floor and lands on her fee

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