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555-605 (Medium)|   Sequences|   Statistics and Sets Problems|                              
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GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
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OG Question Code: PS06558
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Bunuel
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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bagad.07
OG Question Code: PS06558

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Thank you! Added to the first post.
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Sn = n/2(2a+(n-1)d)
S52 = 52/2 (2(1)+(52-1)(1)) = 1378

Answer is C.
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Sn = n/2(2a+(n-1)d)
S52 = 52/2 (2(1)+(52-1)(1)) = 1378

Answer is C.
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The series of the weekly saving is
n, n+1 ,n+2... So, 1,2,3,4...52(n+51)
Where n =1

After 52 weeks she will have the total savings, so,
The sum from 1 to 52 inclusive =1378
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Alternative approach to AP
Bigred2008
In the first week of the Year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756
Notice the last digits from 1 to 10 pair up:
  • (1, 9) → last digit 0
  • (2, 8) → last digit 0
  • (3, 7) → last digit 0
  • (4, 6) → last digit 0
  • This leaves us with 5 .
The sum of the last digits from 1 to 10 is: 0 + 0 + 0 + 0 + 5 + 0 = 5
This pattern of last digits repeats every 10 numbers. From 1 to 50, there are 5 such cycles.

  • 5 cycles × (last digit 5) = last digit 5
Now, add the last two numbers in the sequence, 51 and 52. We only care about the last digit.
  • Last digit from 1-50: 5
  • Add 51 → last digit becomes 6 (5 + 1)
  • Add 52 → last digit becomes 8 (6 + 2)
Conclusion:
The total amount Nancy saved must have a last digit of 8. Options C

NOTE - This should take you hardly 10 seconds after reading the question to eliminate through options
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Bigred2008
In the first week of the Year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756





Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

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