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⇒ 1/10 % of 50
= 1/10 x 1/100 x 50
= 0.05
Which of the following statements are true?
I. If a positive number X is increased by 20% the resulting number would be 1.2X
II.If a positive number X is decreased by 20 % the resulting number would be 0.8X
III.32% of 24 is less than 24% of 32.
A positive number Y is first increased by 10% then decreased by 50% and then increased by 100%. The series of successive changes to Y is equivalent to a single change of
Let the number be 100
10% of 100 is 10 = 110 (new Number)
50% of 110 is 55 = 11055 = 55 (New Number)
100% of 55 is 55= 55+55= 110 (Final Number)
Final Number Initial Number =110100=10
And 10 is 10% of 100
Restaurant A and Restaurant B decides to roll out a new plan which they believe will get them new customers. Restaurant A decides to give a 10% discount on the original bill amount, and then applies 15% tax on the discounted bill. Restaurant B, on the other hand applies a 15% tax on the original bill amount and then gives a 10% discount on the taxed bill.
If the original bill amount is same for both restaurants, which of the following must be true?
Let the billing amount is 100
Case 1
10% discount on 100 = 10,
So 90 is the taxable amount
15% tax on 90= 13.5.
So total Bill = 90+13.5= 103.5 for Restaurant A
Case 2
15% tax on 100= 115
10 % discount on this is 11.5
Total Bill= 11511.5= 103.5 for Restaurant B
Hence same in both case
If 10 is 5 percent of 10 percent of a number, what is 25% of this number?
Step 1: Let the number be x.
Therefore 10% of x = (10/100)*x = 0.1*x
5% of (10% of x) = (5/100)*0.1*x = 0.05*0.1*x = 0.005*x
Given that this value is equal to 10.
Step 2: Finding required values
Therefore,
0.005*x = 10
⇒ x = (10/0.005) = (10000/5)
⇒ x = 2000
Step 3: Calculating final answer
Therefore, 25% of x = (1/4)*2000 = 500.
Correct Answer: D
Karen bought items A, B and C from a supermarket for a total price of $1500. What was the price of item C?
(1) The money she spent to buy item A was 140% of the money she spent to buy the other two items
(2) Item B was 75% less expensive than item C
Steps 1 & 2: Understand Question and Draw Inferences
Let the prices of the items A, B and C be a, b and c dollars respectively.
Given: a + b + c = 1500 . . . Equation 1
We need to find the value of c.
Step 3: Analyze statement 1
As per Statement 1:
The money she spent to buy item A was 140% of the money she spent to buy the other two items
a=140%of(b+c)a=140/100(b+c)a=7/5(b+c)...Equation2
By substituting Equation 2 in Equation 1, we will be able to determine the value of (b + c).
But we will not be able to find the value of c alone.
Therefore, Statement 1 is not sufficient.
Step 4: Analyze statement 2
As per Statement 2:
Item B was 75% less expensive than item C
b = c–75 % of c
b = c−75/100c
b=c/4.........Equ3
By substituting Equation 3 in Equation 1, we will get an expression in terms of a and c. We will not be determine a unique value for c.
Therefore, Statement 2 is not sufficient.
Step 5: Analyze Both Statements Together (if needed)
From Statement 1:
a = 7(b + c)/5 . . . Equation 2
From Statement 2:
b = c/4 . . . Equation 3
Substituting Equation 2 in Equation 1:
7(b + c)/5 + b + c = 1500
12(b + c)/5 =1500
Solving this equation, we get:
b + c = 625 . . . Equation 4
Substituting Equation 3 in Equation 4:
(c/4 + c) = 625
5c = 625 x 4
c = 500
Thus, we are able to get a unique value of c by using both the statements together.
Therefore, the correct answer is Option C.
Tom’s salary has increased by 10% to $11,000. Mike’s salary has reduced by 5%. What is Mike’s current salary if his old salary was two times Tom’s old salary?
Step 1: Question statement and Inferences
We are given that the salary of Tom has increased by 10%, and now it has become $11,000, whereas the salary of Mike has decreased by 5%.
It is also given that the old salary of Mike was twice that of Tom's old salary.
Let Tom’s old salary = T_{O }
Let Mike’s old salary = M_{O} and Mike’s new salary = M_{N}
We need to find the value of M_{N}
Step 2: Finding required values
T_{O} + 10% of T_{O} = 11000
⇒ 1.1* T_{O} = 11000
⇒ T_{O} = 10000
Therefore Tom’s old salary = $10,000
It is also given that Mike’s old salary is twice Tom’s old salary.
⇒ M_{O} = 2 * T_{O} = 20000
Mike’s current salary is 5% less than his old salary.
M_{N} = M_{O} – 5% of M_{O}
⇒ M_{N} = 0.95*M_{O}
⇒ M_{N} = 0.95 * 20000 = 19000
Step 3: Calculating final answer
Therefore Mike’s current salary = $19,000
Correct Answer: B
During a housing slump, the number of houses for sale increases by 50% every month. What is the percentage increase in the number of houses on sale after 3 months?
Step 1: Question statement and Inferences
We are given that during a housing slump, the number of houses for sale increases by 50% every month.
Let the initial number of houses for sale = x
We need to find the number of houses for sale at the end of 3 months to be able to calculate the required percentage increase.
Step 2: Finding required values
Therefore number of houses for sale at the end of the first month = x + 50 % of x=1.5x
Similarly number of houses for sale at the end of the second month = 1.5×(1.5x)=(1.5)^{2}x
Similarly number of houses for sale at the end of the third month = (1.5)^{3} x = 3.375x
Step 3: Calculating the final answer
Therefore absolute increase in the number of houses = 3.375x−x=2.375x
Therefore the percentage increase in the number of houses compared to the initial number = 2.375x/x×100=237.5%
Correct Answer: E
If the tuition fees of University A increased by 25% in four years to $100,000 in the year 2012, by what percent did the tuition fees of University B increase from 2008 to 2012?
(1) In the year 2008, the tuition fees of University A was 2.5 times the tuition fees of University B.
(2) In the year 2012, the tuition fees of University A is $30,000 more than the tuition fees of University B.
Steps 1 & 2: Understand Question and Draw Inferences
Let tuition fees of University A in 2008 and 2012 be A_{0 }and A_{1 }respectively
Let tuition fees of University B in 2008 and 2012 be B_{0 }and B_{1 }respectively
It is given that:
A_{1} = $100,000
And that:
Thus, we have inferred the values of A_{0} and A_{1} from the question statement.
The question asks us about the percent increase in the tuition fees of University B.
In order to find this percent increase, we need:
(i) Either the values of B_{0} and B_{1}.
(ii) Or, a relationship of the form B_{0} = kB_{1} where k is a constant
Step 3: Analyze statement 1
As per Statement 1,
In the year 2008, the tuition fees of University A was 2.5 times the tuition fees of University B.
A_{0} = 2.5 (B_{0}) _{ }
Since we know the value of A_{0}, from the above equation, we will be able to find the value of B_{0}.
However, this statement provides us no clue about the value of B_{1} or even about the relationship between B_{0} and B_{1}.
Thus, Statement 1 is not sufficient.
Step 4: Analyze statement 2
As per Statement 2,
In the year 2012, the tuition fees of University A is $30,000 more than the tuition fees of University B
A_{1} = B_{1} + 30,000
B_{1} = 100,000 – 30,000
B_{1} = 70,000
However, Statement 2 gives us no idea about the value of B_{0} or even about the relationship between B_{0} and B_{1}.
Therefore, Statement 2 is Not Sufficient.
Step 5: Analyze Both Statements Together (if needed)
From Statement 1:
A_{0} = 2.5 (B_{0})
80000 = 2.5 (B_{0})
Thus, _{ }
B_{0} = 32,000
From Statement 2:
B_{1} = 70,000
Thus, we now know the value of B_{0} and B_{1}.
So, we will be able to calculate the percent increase in the tuition fees of University B from 2008 to 2012.
Thus, both the statements together are sufficient to arrive at a unique solution.
Answer: Option (C)
In her second attempt of a standardized test, Joan scored 20 percent higher than her first attempt. How much did she score in her second attempt?
(1) Joan scored 200 in her first attempt.
(2) The absolute difference between her two scores was 40 units.
Steps 1 & 2: Understand Question and Draw Inferences
Given that Joan gave two attempts at a standardized test.
Let her score in her first attempt = F.
Given that her score in her second attempt = F + 20% of F = 1.2F
We need to find the value of F to be able to determine her score in the second attempt.
Step 3: Analyze Statement 1
This statement says that Joan scored 200 in her first attempt.
Therefore we can calculate her score in her second attempt = 1.2F
Therefore statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
This statement says that the absolute difference between her scores in the first and second attempts is 40 units.
Since we obtained the value of F, we can calculate the value of 1.2F.
Therefore statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
Since we arrived at a unique answer in step 3 and step 4 above, this step is not needed.
Correct Answer: D
If Rony’s team played 50% of the total 80 matches conducted in a tournament, what percentage of the matches played by Rony’s team did the team win? (Assume that win and loss are the only possible outcomes. None of the matches ended up in a tie.)
(1) Rony’s team won 60% of the first 30 matches played by them and also won all the remaining matches
(2) The number of matches won by Rony’s team is 133% more than the number of matches lost
Steps 1 & 2: Understand Question and Draw Inferences
Given that total matches played in the tournament = 80.
Number of matches played by Rony’s team (T) = 50% of 80 = 40.
Let the number of matches won by Rony’s team = W.
We need to find the win percentage of Rony’s team = (W/T)*100 = (W/40) * 100
Therefore we need to find the value of W to calculate the win percentage.
Step 3: Analyze Statement 1
The statement says that Rony’s team won 60% of the first 30 matches and then won all of the remaining 10 matches played by them.
So the number of matches won by Rony’s team = W = (60% of 30) + 10 = 18 + 10 = 28.
We know the value of W and therefore we can calculate the required win percentage of Rony’s team.
Therefore Statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
The statement says that number of matches won by Rony’s team is 133% more than the number of matches lost by them.
Since the total number of matches is 40, the number of matches lost = (40 – W).
Therefore
W = (40 – W) + 133% of (40 –W)
(Note that since 33% is equivalent to 1/3, 133% is equivalent to 4/3)
Therefore statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We arrived at a unique answer in step 3 and step 4 above. So this step is not needed.
Correct Answer: D
Jack made a withdrawal from his savings account to fund a medical emergency. What was the percent decrease in his savings fund, if his savings fund post withdrawal will need to be increased by 25 percent to be restored to its initial amount?
Step 1: Question statement and Inferences
Let the withdrawal from the fund be p%
Let the initial amount be X
Balance after withdrawal = B = X p% of X
Step 2: Finding required values
We are also given that B needs to be increased by 25% to bring it back to X.
Step 3: Calculating the final answer
Substitute Equation (1) in Equation (2):
5(100−p)=400500–5p=4005p=100p=20%
Thus, the withdrawal from the fund was 20%
Answer: Option (B)
The number of students in a class is 25, of which 40% are girls. How many more girls must be added in the class such that the percentage of girls is double the current percentage?
Step 1: Question statement and Inferences
The important thing to keep in mind in this question is that when more girls are added to the class, the total number of students will also increase.
Step 2: Finding required values
Originally:
Number of girls = G = 40% of 25
G = 40/100 × 25
G = 10
After adding more girls:
Let x number of girls be added
So, number of girls now =G' = 10 + x
Total number of students now = 25 + x
Step 3: Calculating the final answer
It’s given that:
Thus, the number of girls added = 50
Looking at the answer choices, we see that Option E is correct
Last year country X won 15 gold medals in total 60 competitions. This year country X won only 5 gold medals in a total of 50 competitions. What is the percentage reduction in the percentage of gold medals won per competition this year vs last year?
Step 1: Question statement and Inferences
We are given that last year country X won 15 gold medals in a total of 60 competitions. However, this year country X won only 5 gold medals in a total of 50 competitions.
We have to find the percentage reduction in the percentage of gold medals won per competition.
Step 2: Finding required values
Now, to calculate the required percentage reduction, we need to first calculate the percentage of gold medals won by country X this year and the similar percentage for last year.
Percentage of gold medals (to competitions) this year = (5/50)*100 = 10%
Percentage of gold medals (to competitions) last year = (15/60)*100 = 25%
Step 3: Calculating final answer
We are talking about the reduction in percentage compared to last year.
Therefore the required percentage = [(25 – 10)/25]*100 = 15*4 = 60%
Correct Answer: C
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