In an experiment, half of the participants received only drug X, while

Question

In an experiment, half of the participants received only drug X, while the other half received only a placebo. Before the researcher could conduct the next phase of the study, d participants dropped out. Was the number of dropouts from the group that received drug X greater than the number of dropouts from the group that received the placebo?

(1) The number of dropouts from the group that received the placebo was 4 more than two-thirds of the number of dropouts from the group that received Drug X.

(2) The group that received Drug X had 50 participants at the beginning of the experiment, and fewer than 12 of those participants dropped out.

langyuwang · Answer

Really dont know how to get the IMO C; any help?

Aeyvei · Answer

In an experiment, half of the participants received only drug X,  let's say X
 
 while the other half received only a placebo  let's say Y . 
Before the researcher could conduct the next phase of the study, d participants dropped out.  SO, X + Y - D 
Was the number of dropouts from the group that received drug X greater than the number of dropouts from the group that received the placebo?  Let's say Dx > DY?

(1) The number of dropouts from the group that received the placebo was 4 more than two-thirds of the number of dropouts from the group that received Drug X.

Dy = 4 + (2/3)Dx
Not sufficient

(2) The group that received Drug X had 50 participants at the beginning of the experiment, and fewer than 12 of those participants dropped out.

X = 50
Dx <12, at max 11
Not sufficient

C) Dy = 4 + (2/3)Dx
We have restrictions on Dx, let's test numbers:
Since Dy has to be an integer RHS should be an integer; so Dx needs to be multiple of 3 but less than 12 
Dy = 4 + (2/3)9 = 10 
Dy = 4 + (2/3)6 = 8 
Hence, a conclusive answer

Just checking for c-trap
Dy = 4 + (2/3)12 = 12, so we do need statement 2 to set the restrictions.

VeritasKarishma   Bunuel  That's how I approached it but it took me around 3 minutes, how do I approach is more efficiently? These questions in general.

KarishmaB · Answer

We need to find whether dropouts from Drug X grp > dropouts from placebo grp (1) The number of dropouts from the group that received the placebo was 4 more than two-thirds of the number of dropouts from the group that received Drug X. (2/3) Dx + 4 = Dp Now which is greater depends on whether (1/3)rd of Dx is more than 4 or less. If Dx is a big number, its 1/3rd will be big and hence could be greater than 4. In this case Dx > Dp. If Dx is a small number, its 1/3rd will be small too and hence could be less than 4. In this case Dx < Dp. Not sufficient alone. (2) The group that received Drug X had 50 participants at the beginning of the experiment, and fewer than 12 of those participants dropped out. Dx belongs to the range 0 to 11. Dx must be an integer. No idea about Dp. Not sufficient alone. Taking both together, for 2/3rd of Dx to be an integer, Dx must be a multiple of 3. So Dx can be 3 or 6 or 9. Let's check for 9. (1/3)*9 = 3 which is less than 4. So Dx < Dp. 1/3 of other two numbers will be even smaller so in every case Dx < Dp. Sufficient Answer (C) Aeyvei - What you did is perfectly fine. Just try to do it all orally.

Hoozan · Answer

KarishmaB  please could you explain the logic behind focusing on 1/3rd Dx? Dp depends on 2/3rd of Dx, right? So why aren't we focusing on that aspect?

KarishmaB · Answer

Dp = 2/3rd of Dx + 4
Dx = 2/3rd of Dx + 1/3rd of Dx

Now, what will decide whether Dp is less than, equal to or more than Dx?

Dp already has 2/3rd of Dx. It has another 4. We need to compare 4 with 1/3rd of Dx.

If 4 is equal to 1/3rd of Dx, i.e. Dx is 12, then both Dp and Dx will be equal. (If Dx = 12, Dp = (2/3)*12 + 4 = 12)
If 4 is more than 1/3rd of Dx, Dp is greater i.e. if Dx is less than 12, then Dp is greater (If Dx is say 9, Dp = (2/3) * 9 + 4 = 10)
If 4 is less than 1/3rd of Dx, Dp is smaller i.e. if Dx is greater than 12, then Dp is smaller (if Dx is say 15, Dp = (2/3) * 15 + 4 = 14)

Hoozan · Answer

KarishmaB Wow! This was such a cool way of looking at the sum. Thanks a lot

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In an experiment, half of the participants received only drug X, while

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