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16 Feb 2023, 11:24
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
55% (01:53) correct
45%
(01:32)
wrong
based on 64
sessions
History
Date
Time
Result
Not Attempted Yet
16 Feb 2023, 11:51
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Is \(p > q\)?
(1) \(p^2 > q\).
Not sufficient.
(2) \(p^3 <q\)
Not sufficient.
(1)+(2) We have \(p^3 < q < p^2\). Now, \(p^3 < p^2\) means that either \(p < 0\) or \(0 < p < 1\).
Not sufficient.
Answer: E.
(1) \(p^2 > q\).
- If p = 1 and q = 0, then p > q and the answer is YES.
If p = -1 and q = 0, then p < q and the answer is NO.
Not sufficient.
(2) \(p^3 <q\)
- If p = 1/2 and q = 1/3, then p > q and the answer is YES.
If p = -1 and q = 0, then p < q and the answer is NO.
Not sufficient.
(1)+(2) We have \(p^3 < q < p^2\). Now, \(p^3 < p^2\) means that either \(p < 0\) or \(0 < p < 1\).
- If p = -1 < 0, then we'd have -1 < q < 1. In this case q can be 0 and we'd get that p < q.
If 0 < (p = 1/2) < 1, then we'd have 1/8 < q < 1/4. In this case q can be 1/6 and we'd get that p > q.
Not sufficient.
Answer: E.
16 Feb 2023, 12:06
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TBT
Does p lie to the right of q on a number line?
---------- q ----------- p -----------
Statment 1
(1) \(p^2 > q\)
We know that p^2 is greater than q. Let's plot p on the number line, let's assume p is less than -1 , so p is negative and \(p^2 \) is positive. q can occupy a position either to the right of p or to the left of p. Hence the statement is not sufficient.
----- \(q\) ---- \(p\) ---- \(q\) -- -1 ----------------- 0 -------------------- 1 ---------- \(p^2\) -----
Eliminate A
Statment 2
(2) \(p^3 <q\)
It's given that p^3 is less than q. Let's plot p on the number line, let's assume p is less than -1
---------- \(p^3\) ----------------------------- p ------------------------------------ -1 ------------------ 0 ----------------
Now, q can be either on the right of p or on the left of p as shown below
---------- \(p^3\) ------------- \(q\) --------------- \(p\) ------------------- \(q\) --------------- -1 ------------------ 0 ---------
Hence, the statement is not sufficient.
Combined
The statement combined don't help either as we can still work with the same region -
---------- \(p^3\) ------------- \(q\) --------------- \(p\) ------------------- \(q\) --------------- -1 ------------------ 0 ------------\( p^2\) ---
Option E
