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17 Jan 2021, 09:50
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
73% (02:42) correct
27%
(02:44)
wrong
based on 181
sessions
History
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Not Attempted Yet
There are four prime numbers written in ascending order. The product of the first three is 4199 and that of the last three is 7429. What is the value of the greatest of the four numbers?
A. 13
B. 17
C. 19
D. 23
E. 29
A. 13
B. 17
C. 19
D. 23
E. 29
There are four prime numbers written in ascending order of magnitude. The product of the first three is 4199 and that of the last three is 7429. Find the largest number and the least number?
17 Jan 2021, 10:55
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Bunuel
Of course, it is easy if you are good at calculations, but still, it will be time-consuming.
We can make use of the options and start with the central value - 19.
If both are divisible by 19, then the answer has to be greater than 19. Here 4199=221*19=13*17*19.
You can clearly say that 23 is the answer.
But if you look at the number properties, you can solve without any calculation.
The options are 13, 17, 19, 23, 27. all are consecutive prime numbers.
Now, the unit's digit is 9 in both the products.
13*17*19=1*9=9...Yes
17*19*23=3*3=9..Yes again
The four numbers could be 13, 17, 19, 23
But let us check for 17, 19, 23, 29
17*19*23..Yes as we have seen above
19*23*29=7*9=3..No
23 is the answer
D
17 Jan 2021, 12:05
Kudos
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Bunuel
Once we know that 4199 is not divisible either by 2, 3, 5, 7 and 11 things become little easy, as we now know that answers could be 23 and 29. Eliminate A, B and C.
From here on we check 13, 17 and 19 for 4199 and 17, 19 and 23 for 7429 OR 17, 19 and 23 for 4199 and 19, 23 and 29 for 7429 by looking at the unit digit values after multiplying them. Later fails to suffice.
Answer D.
