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The sum of five consecutive integers is 35.
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21 Jun 2022, 00:31
21 Jun 2022, 00:31
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The sum of five consecutive integers is 35.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
the value of the greatest of these integers |
9 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
The sum of five consecutive integers is 35.
[#permalink]
27 Jun 2022, 08:53
27 Jun 2022, 08:53
1
Given that the sum of five consecutive integers is 35 and we need to find the Value of the greatest integer to answer the problem
Let's solve the problem using two methods
Method 1: Algebra
Let first integer is n
=> next integer will be n+1, n+2, n+3, n+4
=> Sum of these five integers = n + n+1 + n+2 + n+3 + n+4 = 5n + 10 = 35 (given)
=> 5n = 35-10 = 25
=> n = \(\frac{25}{5}\) = 5
=> Value of the greatest integer = n + 4 = 5 + 4 = 9
=> Quantity A (Greatest Integer = 9) = Quantity B (9)
So, Answer will be C
Method 2: Formula (Arithmetic Series)
Since the integers are consecutive => it is an Arithmetic series or Arithmetic Sequence
And we know that for Arithmetic Series, Mean = Median = Middle Term
=> 3rd term which is middle term = Mean = \(\frac{Sum}{5}\) = \(\frac{35}{5}\) = 7
=> Greatest Integer will be 5th term = 3rd term + 2 = 9
=> Quantity A (Greatest Integer = 9) = Quantity B (9)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Sequence problems
Let's solve the problem using two methods
Method 1: Algebra
Let first integer is n
=> next integer will be n+1, n+2, n+3, n+4
=> Sum of these five integers = n + n+1 + n+2 + n+3 + n+4 = 5n + 10 = 35 (given)
=> 5n = 35-10 = 25
=> n = \(\frac{25}{5}\) = 5
=> Value of the greatest integer = n + 4 = 5 + 4 = 9
=> Quantity A (Greatest Integer = 9) = Quantity B (9)
So, Answer will be C
Method 2: Formula (Arithmetic Series)
Since the integers are consecutive => it is an Arithmetic series or Arithmetic Sequence
And we know that for Arithmetic Series, Mean = Median = Middle Term
=> 3rd term which is middle term = Mean = \(\frac{Sum}{5}\) = \(\frac{35}{5}\) = 7
=> Greatest Integer will be 5th term = 3rd term + 2 = 9
=> Quantity A (Greatest Integer = 9) = Quantity B (9)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Sequence problems
gmatclubot
The sum of five consecutive integers is 35. [#permalink]
27 Jun 2022, 08:53
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