Each of three plants, p1, p2, and p3, photosynthesizes glucose at

Question

Each of three plants,  p_1 ,  p_2 , and  p_3 , photosynthesizes glucose at a constant, characteristic rate measured in molecules per minute. If  p_1  is the ratio of  p_1 's rate to  p_2 's rate and  p_2  is the ratio of  p_2 's rate to  p_3 's rate, is  p_3 's rate the greatest of the three?

(1)  p_1 < p_2

(2)  p_2 < 1

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Rabab36 · Answer

p1=p1rate/p2rate

p2=p2rate/p3rate

staement 1 
p1<p2
implies

p1rate*p2rate<(p2rate)^2

sufficient

statement 2

1<p2
p3rate<p2rate

sufficient

option D correct

bv8562 · Answer

p1 = \frac{p1's \ rate}{p2's \ rate}

p2 = \frac{p2's \ rate}{p3's \ rate}

1) p1<p2

\frac{p1's \ rate}{p2's \ rate} < \frac{p2's \ rate}{p3's \ rate} 
 
 p1's \ rate*p3's \ rate<(p2's \ rate)^2

Multiple possibilities to satisfy the above inequality. Therefore, statement 1 is not sufficient to answer the question. Eliminate A and D.

2) p2<1

From this statement we know that p3's rate is greater than p2's rate. But we do not know anything about p1's rate. Hence, not sufficient. Eliminate B.

3) p1<p2 & p2<1

Since, from statement 2 we know that p3's rate is greater than p2's rate and statement 1 says p1<p2 then p2's rate must be greater than p1's rate in order for this inequality to be true. Thus, this answers our question that p3's rate is greatest of all three. Therefore, our answer is C IMO.

finisher009 · Answer

1. Translate the Ratios:
• p1 = R1 / R2
• p2 = R2 / R3

2. Rephrase the Core Question:
• Is R3>R2 ? This is the same as asking if R2/R3 < 1. So, is p2 < 1?
• Is R3 > R1? This is the same as asking if R1 / R3 < 1. We know R1 = p1 * R2 and `R2 = p2 * R3`. So, `R1 = p1 * p2 * R3`. The question becomes, is `(p1 * p2 * R3) / R3 < 1`? So, is `p1 * p2 < 1`?
2. Our new question: Is `p2 < 1` AND is `p1 * p2 < 1`?

3. Check the Statements:
• (1) `p1 < p2`: Useless alone. `p1=2, p2=3` -> No. `p1=0.5, p2=0.6` -> Yes. Insufficient.
• (2) `p2 < 1`: This tells us `R3 > R2`. But we don’t know about `p1`. If `p1=5` and `p2=0.5`, then `p1*p2 = 2.5 > 1`, so `R1 > R3`. No. If `p1=1.5` and `p2=0.5`, then `p1*p2 = 0.75 < 1`. Yes. Insufficient.

4. Combine (1) and (2):
• We have `p1 < p2` and `p2 < 1`.
• This means `p1 < p2 < 1`. So, both `p1` and `p2` are positive numbers that are less than 1.
• Is `p2 < 1`? Yes, Statement (2) says so.
• Is `p1 * p2 < 1`? Yes, the product of two positive numbers less than 1 is always less than 1.
• Since we get a definitive “Yes” to both conditions, the combined statements are Sufficient.

Each of three plants, p1, p2, and p3, photosynthesizes glucose at

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GMAT Data Sufficiency (DS) Questions

Each of three plants, p1, p2, and p3, photosynthesizes glucose at

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