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Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
21 Apr 2022, 02:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:23) correct
47%
(02:15)
wrong
based on 117
sessions
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The number of 10-digit numbers such that the product of any two consecutive digits in the number is a prime number, is
(A) 2048
(B) 1024
(C) 512
(D) 256
(E) 64
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 2048
(B) 1024
(C) 512
(D) 256
(E) 64
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
05 May 2022, 22:44
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Bunuel
The consecutive numbers can be (1,2) , (1,3), (1,5), (1,7) or (2,1), (3,1), (5,1), (7,1)
If the first digit is 1, 2nd digit can be filled in 4 ways (2,3,5 or 7), third digit will be 1 (filled in 1 way), fourth digit will again be filled in 4 ways, so on
Total no. of ways = 1 * 4 * 1 * 4 *.... = \(4 ^5\) = 1024
If the first place is filled by either 2,3,5 or 7 (4 ways), 2nd digit will be filled in 1 way only (digit 1), third digit can be filled in 4 ways (using 2,3,5 or 7), 4th digit will be filled in 1 way and so on
Total no. of ways = 4 * 1 * 4 * 1 * .... = \(4 ^5\) = 1024
Total no. of ways = 1024 + 1024 = 2048
Option A
05 May 2022, 23:30
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Bunuel
A product will be prime only when one digit is prime and the other is 1. We have 4 prime digits (2, 3, 5, 7).
If every pair of consecutive digits needs to be prime, every prime digit needs to be surrounded by 1s.
So two ways are possible: P 1 P 1 P 1 P 1 P 1 and 1 P 1 P 1 P 1 P 1 P
Each P spot can be filled up in 4 ways.
So total possibilities = 4*4*4*4*4 * 2 = 2^11 = 2048
Answer (A)
