Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
10 Jul 2024, 07:01
Kudos
Bookmarks
P: 5
Q: 3
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (03:04) correct
53%
(03:20)
wrong
based on 548
sessions
History
Date
Time
Result
Not Attempted Yet
The king of Trishkinda has specially designed an ivory dice. Six exotic stones – agate, jasper, chalcedony, sapphire, topaz, garnet – are embedded on the six sides of the dice, such that one side has exactly one type of stone and no two sides have the same type of stone. When the dice is rolled, the probability of the agate stone appearing is \(\frac{1}{6}\). Let there be values P, Q, x, y such that when the dice is thrown P times, the probability of the agate stone appearing all P times is x and when the dice is thrown Q times, the probability of the agate stone appearing all Q times is y. Furthermore, \(x < y\) and \(\frac{1}{x} + \frac{1}{y} = 7,992\).
In the table, select a value for P and a value for Q that are jointly consistent with the given information. Make only two selections, one in each column.
In the table, select a value for P and a value for Q that are jointly consistent with the given information. Make only two selections, one in each column.
|
| P | Q | |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
ShowHide Answer
Official Answer
P: 5
Q: 3
10 Jul 2024, 07:14
Kudos
Bookmarks
Bunuel
Experts' Global Explanation:
Probability of agate stone appearing when the dice is rolled 1 time = (1/6)
Probability of agate stone appearing when the dice is rolled 2 times = (1/6) x (1/6) = (1/6)2
Probability of agate stone appearing when the dice is rolled P times = (1/6)^P = x
Probability of agate stone appearing when the dice is rolled Q times = (1/6)^Q = y
1/x + 1/y = 7992
1/(1/6)^P + 1/(1/6)^Q = 7992
6^P + 6Q = 7992
6^P + 6^Q = 7992
Taking 6Q as the common term:
6^Q(6^(P – Q) + 1) = 7992 (Equation I)
6^Q(1 + 6^(P – Q)) = 7992
6^Q(1 + 6^(P – Q)) = 6 x 6 x 6 x 37
6^Q(1 + 6^(P – Q)) = 6 x 6 x 6 x (1 + 36)
6^Q(1 + 6^(P – Q)) = 6^3 x (1 + 6^2)
Comparing both sides:
Q = 3
P – Q = 2
P – 3 = 2
P = 5
Note that if we had taken 6^P as the common term in Equation I, we would have received P = 3 and Q =5 as the answer. Both (P = 5, Q = 3) and (P = 3 and Q =5) satisfy Equation I, however since the question specifies that x < y, it follows that (1/6)^P < (1/6)^Q, and thus P =5 and Q =3 is the only valid solution.
Hence, for “P” column, “5”, and for “Q” column, “3” is the correct combination of the answer choices.
10 Jul 2024, 07:38
Kudos
Bookmarks
7992 = (6^3) x 37
37=36+1
36=6^2
So, we can write 7992 = (6^3) x (6^2 + 1) = 6^5 + 6^3 equation (i)
x=1/(6^P) and y=1/(6^Q)
We are given that x<y, so we can conclude that Q<P.
Using equation (i), we can assign the values.
P=5 and Q=3
37=36+1
36=6^2
So, we can write 7992 = (6^3) x (6^2 + 1) = 6^5 + 6^3 equation (i)
x=1/(6^P) and y=1/(6^Q)
We are given that x<y, so we can conclude that Q<P.
Using equation (i), we can assign the values.
P=5 and Q=3
