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Difficulty:
15%
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Question Stats:
83% (01:24) correct
17%
(01:42)
wrong
based on 116
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Which of the following number is not the sum of three consecutive odd numbers?
A. 15
B. 75
C. 123
D. 297
E. 313
_________________
A. 15
B. 75
C. 123
D. 297
E. 313
_________________
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Solution
To find:
• Among the given options, which one does not represent the sum of three consecutive odd numbers
Approach and Working:
• Let us assume the least of the consecutive odd numbers is p
- o Therefore, the next 2 odd numbers will be p+2 and p+4
- o This indicates that the final sum will be always divisible by 3, irrespective of the value of p
• Now, among the given options, 313 is a number which is not a multiple of 3
- o Therefore, 313 cannot be the sum of three consecutive odd numbers
Hence, the correct answer is option E.
Answer: E
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Updated on: 20 Jul 2021, 08:18
Originally posted by BrushMyQuant on 20 Jul 2021, 05:41.
Last edited by BrushMyQuant on 20 Jul 2021, 08:18, edited 1 time in total.
Last edited by BrushMyQuant on 20 Jul 2021, 08:18, edited 1 time in total.
Three consecutive Odd Numbers can be taken as n-2, n, n+2
So, their sum becomes n-2 + n + n +2 = 3n
=> Sum of three consecutive odd numbers should be a multiple of 3
Divisibility rule of 3 is Sum of all the digits of the number should be divisible by 3
Let's check all the options choices now
(A) 15 -> Sum of digits = 1+5 = 6 => Divisible by 3 => POSSIBLE
(B) 75 -> Sum of digits = 7+5 = 12 => Divisible by 3 => POSSIBLE
(C) 123 -> Sum of digits = 1+2+3 = 6 => Divisible by 3 => POSSIBLE
(D) 297 -> Sum of digits = 2+9+7 = 18 => Divisible by 3 => POSSIBLE
(E) 313 -> Sum of digits = 3+1+3 = 7 => NOT Divisible by 3 => NOT POSSIBLE
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
_________________
So, their sum becomes n-2 + n + n +2 = 3n
=> Sum of three consecutive odd numbers should be a multiple of 3
Divisibility rule of 3 is Sum of all the digits of the number should be divisible by 3
Let's check all the options choices now
(A) 15 -> Sum of digits = 1+5 = 6 => Divisible by 3 => POSSIBLE
(B) 75 -> Sum of digits = 7+5 = 12 => Divisible by 3 => POSSIBLE
(C) 123 -> Sum of digits = 1+2+3 = 6 => Divisible by 3 => POSSIBLE
(D) 297 -> Sum of digits = 2+9+7 = 18 => Divisible by 3 => POSSIBLE
(E) 313 -> Sum of digits = 3+1+3 = 7 => NOT Divisible by 3 => NOT POSSIBLE
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
_________________
How to Solve :
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
GMAT 1: 760 Q51 V42
Posts: 10,057
The sum of 3 consecutive odd numbers is the multiple of 3.
313 = 3 + 1 + 3 = 7 is not divisible by 3.
Answer E
313 = 3 + 1 + 3 = 7 is not divisible by 3.
Answer E
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