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Jagan212
Joined: 06 Apr 2018
Last visit: 26 May 2024
Posts: 34
Given Kudos: 35
Location: India
Schools: IIMC MBAEx'23 (D) IIMA PGPX'23
GMAT 1: 620 Q43 V32
GPA: 3.2
07 Aug 2020, 20:21
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
61% (03:06) correct
39%
(03:01)
wrong
based on 430
sessions
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Of the four-digit integers greater than 9,000, with the sum of their digits greater than 30, what is the sum of the integers that have two pairs of digits such that digits in one pair are equal to each other and the digits of the other pair are equal to each other but distinct from the other two?
A. 0
B. 9,999
C. 59,328
D. 88,659
E. 270,000
A. 0
B. 9,999
C. 59,328
D. 88,659
E. 270,000
08 Aug 2020, 01:27
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Four-digit integers greater than 9,000 -> This means one of the number has to be 9.(The first digit )
Digits in one pair are equal to each other --> This means another number has to be 9 as well.
First Possible combinations: 99_ _, 9_ 9_ and 9 _ _ 9.
Sum of their digits greater than 30: Two numbers are 9 and 9. So 30-18 = 12 . The sum of remaining two digits should be greater than 12 and and the digits of the other pair are equal -> This means the both the numbers will be same.
Possible combination: 7 + 7 = 14 and 8 + 8 = 16
Placing the digit (7) in first possible combination: 9977, 9797, 9779.
Placing the digit (8) in first possible combination: 9988, 9898, 9889.
Adding all 6 results: 9977 + 9797 + 9779 + 9988 + 9898 + 9889 = 59,328.
Answer C
Digits in one pair are equal to each other --> This means another number has to be 9 as well.
First Possible combinations: 99_ _, 9_ 9_ and 9 _ _ 9.
Sum of their digits greater than 30: Two numbers are 9 and 9. So 30-18 = 12 . The sum of remaining two digits should be greater than 12 and and the digits of the other pair are equal -> This means the both the numbers will be same.
Possible combination: 7 + 7 = 14 and 8 + 8 = 16
Placing the digit (7) in first possible combination: 9977, 9797, 9779.
Placing the digit (8) in first possible combination: 9988, 9898, 9889.
Adding all 6 results: 9977 + 9797 + 9779 + 9988 + 9898 + 9889 = 59,328.
Answer C
General Discussion
07 Aug 2020, 22:16
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Of the four-digit integers greater than 9,000, with the sum of their digits greater than 30, what is the sum of the integers that have two pairs of digits such that digits in one pair are equal to each other and the digits of the other pair are equal to each other but distinct from the other two?
Solution:
four-digit integers greater than 9,000:
9001 to 9999
sum of their digits greater than 30:
Only possible 4 digits are 6,7,8,9
one pair are equal to each other and the digits of the other pair are equal to each other but distinct,
means of 4 digits, 2 different integers have to be selected, that gives us 2 set (9,6) and (8,7)
as total 12 different integers are possible :
9669,9966,9696,6699,6969,6996,8778,8787,8877,7887,,7878,7788
Approximately, answer is 12*9000 = 10800, answer should be greater than 10,800, which is only option E.
Could you please share the solution, how OA is C?
Solution:
four-digit integers greater than 9,000:
9001 to 9999
sum of their digits greater than 30:
Only possible 4 digits are 6,7,8,9
one pair are equal to each other and the digits of the other pair are equal to each other but distinct,
means of 4 digits, 2 different integers have to be selected, that gives us 2 set (9,6) and (8,7)
as total 12 different integers are possible :
9669,9966,9696,6699,6969,6996,8778,8787,8877,7887,,7878,7788
Approximately, answer is 12*9000 = 10800, answer should be greater than 10,800, which is only option E.
Could you please share the solution, how OA is C?
