The numbers in set P denote the distance of certain positive integers from 1 on the number line. The numbers in set Q denote
the distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?
Given:
To Find: the statement, which is true about the standard deviation of sets P and Q
Approach:
Working out:
Answer : A
List A: 20, 4, 8, x
List B: 8, 3, 6, 12, 4
List A above has 4 numbers and List B above has 5 numbers. What is the value of x?
(1) The range of the numbers in List A is equal to the range of the numbers in List B
(2) The median of the numbers in List A is equal to the median of the numbers in List B.
Step 1 & 2: Understand Question and Draw Inference
Given:
To find: x = ?
Step 3 : Analyze Statement 1 independent
(1) The range of the numbers in List A is equal to the range of the numbers in List B
Not sufficient to find a unique value of x.
Step 4 : Analyze Statement 2 independent
(2) The median of the numbers in List A is equal to the median of the numbers
in List B.
Not sufficient to find a unique value of x
Step 5: Analyze Both Statements Together (if needed)
Thus, the two statements together are sufficient to find a unique value of x
Answer: Option C
When positive integer y is added to each of the first n nonnegative integers, which of the following statements is true?
I. If the median of the resulting numbers is then n is odd
II. The arithmetic mean of the resulting numbers is equal to the median of the resulting numbers
III. The arithmetic mean of the resulting numbers is y units greater than the arithmetic mean of the first n positive integers.
Given:
To Find: Which of the 3 statements is/are true?
Approach:
We will first find the expressions for these 3 quantities.
2. Then, we’ll evaluate the 3 statements one by one to determine which is/are true for all values of y and n
Working out:
Looking at the answer choices, we see that the correct answer is Option B
If a, b and c are positive integers, what is the average (arithmetic mean) of a and c?
1. The average of a + b and 4 is 6
2. The average of a + c and b is 18
Step 1 & 2: Understand Question and Draw Inference
Given: Integers a, b, c > 0
To find: (a+c) /2
Step 3 : Analyze Statement 1 independent
Statement 1 says that ‘The average of a + b and 4 is 6’
Step 4 : Analyze Statement 2 independent
Statement 2 says that ‘The average of a + c and b is 18’
Step 5: Analyze Both Statements Together (if needed)
Answer: Option E
In an interstate Mathematics Olympiad, the distribution of the scores obtained by the participating students is symmetric about
the mean m. 68 percent of the distribution lies within one standard deviation d of the mean and 95 percent of the distribution lies
within 2 standard deviations of the mean. If there were 70 students who scored more than Ricky, 428 students who scored less than Ricky and none that scored equal to him, his score must lie between
Given:
To Find:: The range in which Ricky’s score should lie
Approach:
Working out:
Answer : D
The average (arithmetic mean) of the prime numbers that lie between 10 and 20 is how much greater than the average of the
prime numbers that lie between 1 and 10?
Given:
2 sets of Prime Numbers – let’s call them Sets A and B:
To find: Difference between Average(Set B) and Average (Set A)
Approach:
Working out:
Correct Answer – Option B
A group of students was participating in a quizzing competition consisting of 3 rounds. A student had to clear the first round to move into the second round and so on till he cleared all the rounds. What was the median number of the rounds cleared by the students in the quiz?
(1) 20 percent of the students could not clear round 1 of the quiz
(2) 40 percent of the students could clear round 2 but could not clear round 3.
Step 1 & 2: Understand Question and Draw Inference
To Find: Median number of rounds cleared by the students
Step 3 : Analyze Statement 1 independent
Insufficient to find an answer.
Step 4 : Analyze Statement 2 independent
2. 40 percent of the students could clear round 2 but could not clear round 3.
However, we do not know the number of students who cleared round 3 and the number of students who could not clear round 1
Insufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
Let there be a% of students who cleared round 1 and b% of students who cleared round 2
Insufficient to answer.
Answer: E
Arrange the following sets in the order of the increasing magnitude of their mean to standard deviation ratio.
I. {50, 60, 70, 80}
II. {35, 40, 45, 50}
III. {90, 110, 130, 150}
Given:
To Find: Arrange the sets in increasing order of the (Mean / Standard deviation) ratio.
Approach:
Working out:
Answer : D
Set P has n integers. What is the standard deviation of Set P?
(1) The range of Set P is equal to zero
(2) The mean of Set P is equal to the median of Set P
Step 1 & 2: Understand Question and Draw Inference
To Find: Standard Deviation (P)
Step 3 : Analyze Statement 1 independent
(1) The range of Set P is equal to zero
In both the cases, the standard deviation is 0.
Sufficient to answer.
Step 4 : Analyze Statement 2 independent
(2) The mean of Set P is equal to the median of Set P
Insufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step 3, this step is not required.
Answer : A
In triangle ABC (not shown), is the range of the angles of the triangle greater than 90^{o}?
(1) The median angle of triangle ABC is 70^{o}
(2) The difference between the two larger angles of triangle ABC
is 10^{o}
Step 1 & 2: Understand Question and Draw Inference
Given: A triangle ABC
To find: Is z – x > 90^{o} ?
Step 3 : Analyze Statement 1 independent
(1) The median angle of triangle ABC is 70^{o}.
But we do not know if x < 10^{o} . So, Statement 1 alone is not sufficient.
Step 4 : Analyze Statement 2 independent
(2) The difference between the two larger angles of triangle ABC is 10^{o}
But we do not know if So, Statement 2 alone is not sufficient.
Step 5: Analyze Both Statements Together (if needed)
Since we now know the values of x, y and z, we’ll be able to answer the question on the range of the angles.
The two statements together are sufficient to answer the question.
Set P consists of 10 positive integers arranged in order of increasing magnitude. The difference between any two successive
terms of the set is 4. If the two largest terms of the set are removed, what is the decrease in the average(arithmetic mean) of
the set?
Given:
To Find: Decrease in the average of the set after removal of (a+9d) and (a+8d)
Approach:
Working out:
Hence, the average decreased by 4 units.
Answer : C
A is the average (arithmetic mean) of the first 7 multiples of 3 and B is the median of the first 3 multiples of positive integer n. If the
value of A^{2} – B^{2} is zero, what is the value of n?
Given:
To Find: n =?
Approach:
Working out:
Looking at the answer choices, we see that the correct answer is Option D
Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?
(1) The sum of A×10^{4} , B×10^{2} and C is divisible by 9
(2) The product of the range of Set P and the median of Set P is 18.
Step 1 & 2: Understand Question and Draw Inference
Given:
To find: Is divisible by 3?
Step 3 : Analyze Statement 1 independent
Sufficient.
Step 4 : Analyze Statement 2 independent
Thus, Statement 2 is not sufficient to provide a unique answer to the posed question.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 3, this step is not required.
Answer: Option A
A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to the
arithmetic mean of the n integers?
(1) The sum of any 3 successive integers of the set is divisible by 3
(2) The difference between any 2 successive integers of the set is 4
Step 1 & 2: Understand Question and Draw Inference
Given: A set of n distinct integers, arranged in the order of increasing magnitude
To find: Is Median = Mean?
The median is equal to the mean if:
Step 3 : Analyze Statement 1 independent
(1) The sum of any 3 successive integers of the set is divisible by 3
Step 4 : Analyze Statement 2 independent
(2) The difference between any 2 successive integers of the set is 4
So Statement 2 is sufficient.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 4, this step is not required
Answer: Option B
Set A consists of 15 positive integers. Is the mean of set A equal to the median of set A?
(1) The integers in set A, when arranged in the order of increasing magnitude, are not evenly spaced
(2) If an integer x, which is equal to the mean of set A, is added to the set, the median of the set does not
change
Step 1 & 2: Understand Question and Draw Inference
To Find: Is Mean (A) = Median (A)
Step 3 : Analyze Statement 1 independent
Insufficient to answer.
Step 4 : Analyze Statement 2 independent
2. If an integer x, which is equal to the mean of set A, is added to the set, the median of the set does not change
Step 5: Analyze Both Statements Together (if needed)
Combining the two statements does not give us any extra information to answer the question.
Insufficient to answer.
Answer : E
A merchant sold 32 antique items for $28800. If his profit margin was 20%, then his average cost per antique item was
Given:
To Find: Average cost per item
Approach:
2. We’re given the total selling price of all items as well as the profit margin. Using these 2 pieces of information together, we can find the total cost price of all 32 items
Working out:
Looking at the answer choices, we see that the correct answer is Option B
List A contains 16 distinct odd integers and 9 distinct even integers such that the average (arithmetic mean) of List A is 13.84. If each odd integer is doubled in magnitude, what is the new average (arithmetic mean) of List A?
(1) The average (arithmetic mean) of the even integers in List A is 10
(2) Before each odd integer is doubled in magnitude, the smallest odd integer in List A is 1 and the largest odd integer in List A is
31.
Step 1 & 2: Understand Question and Draw Inference
So, in order to answer this question, we need to know the value of D.
Step 3 : Analyze Statement 1 independent
(1) The average (arithmetic mean) of the even integers in List A is 10
Putting (2) in (1), we get the value of D.
So, Statement 1 alone is sufficient.
Step 4 : Analyze Statement 2 independent
(2) Before each odd integer is doubled in magnitude, the smallest odd integer in
List A is 1 and the largest odd integer in List A is 31
So, Statement 2 alone is sufficient.
Step 5: Analyze Both Statements Together (if needed)
Since we get a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
While debugging a piece of software, an engineer records the number of bugs he finds each day. If the number of bugs found by the engineer reduces by x with each passing day, what is the standard deviation of the number of bugs found by the engineer during the last 7 days?
(1) The difference between the maximum number of bugs and the minimum number of bugs found by the engineer during the last 7
days is 24.
(2) The average (arithmetic mean) number of bugs found by the engineer during the last 7 days is 24
Step 1 & 2: Understand Question and Draw Inference
To Find: standard deviation of the number of bugs found during the last 7 days
Step 3 : Analyze Statement 1 independent
Sufficient to answer
Step 4 : Analyze Statement 2 independent
2. The average (arithmetic mean) number of bugs found by the engineer during the last 7 days is 24
1 equation 2 variablesà cannot find a unique value of x.
Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
Since, we have a unique answer from step 3, this step is not required.
Answer: A
A group of 4 boys and 5 girls take a test. What is the average (arithmetic mean) score of the group in the test?
Step 1 & 2: Understand Question and Draw Inference
Given: 4 boys and 5 girls take a test
To find: The Average score of the group
Step 3 : Analyze Statement 1 independent
Statement 1 says that ‘The average score of the boys is 23 points while the average score of the girls is 20 points’
Step 4 : Analyze Statement 2 independent
Statement 2 says that ‘If one of the girls had scored 6 points more, the average score of the group would have been 22’
Let the girl who scored 6 points be the first girl (in the list of scores). So, her new score = G + 6
So, Statement 2 is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
The table above shows the distribution of the distance, rounded to the nearest integer, run by 20 athletes in a marathon. Which of the
following cannot be the approximate average (arithmetic mean) distance run (in kilometres) by the athletes in the marathon?
Given:
To Find: The option that cannot be the average distance run by the athl
Approach:
Working out:
Answer : E
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