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13 Dec 2023, 07:00
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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:
75%
(hard)
Question Stats:
65% (02:38) correct
35%
(02:34)
wrong
based on 296
sessions
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
Lisa wrote down 10 consecutive integers on a blackboard. However, Bart, being mischievous, erased one of them. If the sum of the remaining nine numbers is 146, what is the value of the number that Bart erased?
A. 7
B. 9
C. 12
D. 19
E. 21
Lisa wrote down 10 consecutive integers on a blackboard. However, Bart, being mischievous, erased one of them. If the sum of the remaining nine numbers is 146, what is the value of the number that Bart erased?
A. 7
B. 9
C. 12
D. 19
E. 21
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16 Dec 2023, 07:25
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GMAT Club Official Explanation:
Lisa wrote down 10 consecutive integers on a blackboard. However, Bart, being mischievous, erased one of them. If the sum of the remaining nine numbers is 146, what is the value of the number that Bart erased?
A. 7
B. 9
C. 12
D. 19
E. 21
Assume the smallest of the 10 consecutive integers is x. Then their sum is:
- x + (x + 1) + ... + (x + 9) = 10x + (1 + 2 + ... 9) = 10x + (1 + 9)/2*9 = 10x + 45.
Now, let's assume Bart erased the number k. Then, we'd have:
- 10x + 45 = 146 + k;
10x = 101 + k.
Since x is an integer, the left-hand side of the equation is a multiple of 10. Therefore, the right-hand side must also be a multiple of 10, which means the units digit of k must be 9. This narrows our options down to B (9) and D (19). However, k cannot be 9 because in that case x would be 11, and the erased number cannot be smaller than the smallest number in the set. Therefore, Bart must have erased the number 19.
Answer: D.
General Discussion
13 Dec 2023, 07:33
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The numbers have to be evenly spaced so the median must be close to the average of the 9 numbers avg is 146/9=16.22 closest to 19.Now to confirm just add 10 consecuitve integers and see for which solution exists.
Let the integers be x,x+1...........x+9
For case of 19
10x+45=19+146
x=12
so the series is 12 13 14 15........................
Since D there is 19 so it's the answer.
For other options the answer of x wont be an integer so rejected.
Let the integers be x,x+1...........x+9
For case of 19
10x+45=19+146
x=12
so the series is 12 13 14 15........................
Since D there is 19 so it's the answer.
For other options the answer of x wont be an integer so rejected.
