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24 Jan 2020, 21:16
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (02:00) correct
24%
(02:08)
wrong
based on 176
sessions
History
Date
Time
Result
Not Attempted Yet
What is the summation of the all 2-digit numbers that are divided by 3?
a. 111
b. 1665
c. 0
d. 1531
e. 1247
a. 111
b. 1665
c. 0
d. 1531
e. 1247
24 Jan 2020, 22:53
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Bookmarks
Question:
What is the summation of all the 2-digit numbers that are divisible by 3?
Solution:
The first 2 digit number is 12 = 3 * 4
The first 2 digit number is 99 = 3 * 33
The number of such terms = 33-4+1 = 30
Thus, required sum
= 3*4 + 3*5 + ... 3*33
= 3(4 + 5 + ... 33)
Since the numbers 4,5,6... Have a constant difference between consecutive terms (i.e. are in Arithmetic Progression), the sum can be calculated as:
Sum of 4,5,6,...33
= Mean * Number of terms
= [(1st term + Last term)/2] * (Number of terms)
= [(4+33)/2] * 30
= 37*15 = (37*3)*5
= 111*5 = 555
Thus, the required sum
= 3(4 + 5 + ... 33)
= 3 * 555
= 1665
Answer B
Note: The answer options aren't so well thought of. First, they should be in ascending order.
Next, it's too easy to decide the answer by looking at the options - only 111 and 1665 are multiples of 3; of which 111 is just too small.
Third, what is 0 doing as an option here!!!
Posted from my mobile device
What is the summation of all the 2-digit numbers that are divisible by 3?
Solution:
The first 2 digit number is 12 = 3 * 4
The first 2 digit number is 99 = 3 * 33
The number of such terms = 33-4+1 = 30
Thus, required sum
= 3*4 + 3*5 + ... 3*33
= 3(4 + 5 + ... 33)
Since the numbers 4,5,6... Have a constant difference between consecutive terms (i.e. are in Arithmetic Progression), the sum can be calculated as:
Sum of 4,5,6,...33
= Mean * Number of terms
= [(1st term + Last term)/2] * (Number of terms)
= [(4+33)/2] * 30
= 37*15 = (37*3)*5
= 111*5 = 555
Thus, the required sum
= 3(4 + 5 + ... 33)
= 3 * 555
= 1665
Answer B
Note: The answer options aren't so well thought of. First, they should be in ascending order.
Next, it's too easy to decide the answer by looking at the options - only 111 and 1665 are multiples of 3; of which 111 is just too small.
Third, what is 0 doing as an option here!!!
Posted from my mobile device
22 Feb 2024, 12:57
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sujoykrdatta
I don't understand why 0 is wrong...the question asks for all 2-digit numbers divisible by three, not all positive 2-digit numbers divisible by three. If we include the negative numbers into the summation, it would be 0.
Why shouldn't we include negative numbers?
