The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180II. When B is divided by 60, the remainder is 30III. The value of the decimal digits is greater in the number than in the numbera)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'B'. Can you explain this answer?

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I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180

II. When B is divided by 60, the remainder is 30

III. The value of the decimal digits is greater in the number

than in the number

a)
I only
b)
II only
c)
III only
d)
I and II only
e)
I and III only

Correct answer is option 'B'. Can you explain this answer?

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The arithmetic mean (average) of a set of 5 numbers is an integer A. U...

Let the set of 5 numbers be {p, q, r, s, t}
Arithmetic Mean of this set = A

A is an integer
A = 180q + 30, where quotient q is an integer
When 2 numbers in the set are decreased by 120 and 180, the new Arithmetic Mean is B

To find: Which of the 3 statements is/are true?

Approach:

Looking at the statements, we realize that to answer the question, we need to find an equation for B (to find the remainder that B leaves with certain divisors) and also a relation between A and B
We’ll use the given information to find these 2 information points
- Since we are given the decrease in 2 numbers of the set, we can find the total decrease in the sum of the 5 numbers (with respect to the original sum of the 5 numbers). By expressing the original sum of the 5 numbers and the decreased sum in terms of A and B respectively, we can find a relation between A and B
- Since we know an equation for A, we can use the relation between A and B to find an equation for B.
Then, we’ll evaluate the 3 statements one by one.
Working Out:
Finding a relation between A and B
- When 2 numbers in the set are decreased by 120 and 180, the new Arithmetic Mean is B
  - 120 + 180 = 300
- So, when the sum p +q + r + s + t is decreased by 300, the new mean is B

Thus, B = A – 60

Evaluating Statement I
The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180
- The remainder that A leaves with 180 is 30
- From the equation B = 180(q-1) + 150, it is clear that the remainder that B leaves with 180 is 150
- Since 150 is greater than 30, Statement I is not true.

Evaluating Statement II
When B is divided by 60, the remainder is 30
- Rearranging the equation B = 180(q-1) + 150:
  - B = 180(q-1) + 120 +30
  - B = {180(q-1) + 120} + 30
- From the above form of the equation, it’s clear that when B is divided by 60, the term {180(q-1) + 120} will be divisible by 6. The leftover term, 30, is positive and is less than the divisor 60. So, it passes both the tests for being a remainder.
- Therefore, when B is divided by 60, the remainder is 30
- Statement II is true.
Evaluating Statement III
The value of the decimal digits is greater in the number than in the number
A = 180q + 30
So, when A is divided by 90, the term 180q is divisible by 90. The decimal digits come from the part
B = 180(q-1) + 150 = {180(q-1) + 90} + 60
So, when B is divided by 90, the term {180(q-1) + 90} is divisible by 90. The decimal digits come from the part
Therefore, the value of the decimal digits is greater in
So, Statement III is not true.
Getting to the answer
- Thus, we see that only Statement II is true.

Looking at the answer choices, we see that the correct answer is Option B

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The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180II. When B is divided by 60, the remainder is 30III. The value of the decimal digits is greater in the number than in the numbera)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'B'. Can you explain this answer?

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The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180II. When B is divided by 60, the remainder is 30III. The value of the decimal digits is greater in the number than in the numbera)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180II. When B is divided by 60, the remainder is 30III. The value of the decimal digits is greater in the number than in the numbera)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180II. When B is divided by 60, the remainder is 30III. The value of the decimal digits is greater in the number than in the numbera)I onlyb)II onlyc)III onlyd)I and II onlye)I and III onlyCorrect answer is option 'B'. Can you explain this answer?.

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