Gerald and James each had a few one dollar bills. After James gave 16 one dollar bills to Gerald, the ratio of the number of bills that James and Gerald respectively had was 14/11 Gerald now returned 8 one dollar bills to James, thereby increasing the ratio of the number of bills that James and Gerald respectively had to 16/9 What was the ratio of the number of bills that James and Gerald respectively had originally?
Given:
To Find: J/g = ?
Approach:
Working out:
Looking at the answer choices, we see that the correct answer is Option A
The revenue of a company is directly proportional to the number of customers it serves, which in turn is directly proportional to the
marketing spend of the company. What is the revenue of the company if it spends one million dollars in marketing?
(1) If the company spends $250,000 in marketing, it earns a revenue of ten million dollars
(2) The ratio of revenue of the company to the number of customers it serves is 4:1
Step 1 & 2: Understand Question and Draw Inference
Given: Let revenue = R, Number of customers = C and marketing spend = M
Step 3 : Analyze Statement 1 independent
Thus, Statement 1 alone is sufficient to answer the question.
Step 4 : Analyze Statement 2 independent
Since we don’t know the value of p yet, we cannot find the value of product kp Thus, Statement 2 alone is not sufficient to answer the 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 store stocks shirts, trousers and suits in the ratio of 4:5:6. If the store stocks only these 3 items, what is the number of items
stocked in the store?
(1) The number of suits is 100 more than the number of shirts stocked in the store
(2) The number of suits is 150 less than the number of shirts and trousers stocked in the store
Step 1 & 2: Understand Question and Draw Inference
Let the number of shirts, trousers and suits be 4x, 5x and 6x respectively.
Total number of items = 4x +5x+6x = 15x.
To find: 15x = ?
To answer this question, we need to find the value of x
Step 3 : Analyze Statement 1 independent
6x – 4x = 100
i.e. 2x = 100
x = 50
Sufficient to answer
Step 4 : Analyze Statement 2 independent
2. The number of suits is 150 less than the number of shirts and trousers stocked in the store
(4x +5x) – 6x = 150
3x = 150
x = 50
Sufficient to answer
Step 5: Analyze Both Statements Together (if needed)
Since, we have a unique answer from steps 3 and 4, this step is not required.
Answer: D
A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4^{th} of the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?
Given:
To Find: Initial number of books in the library
Approach:
Working out:
a. So, we have 3l + 150 = 5s, i.e. 5s – 3l = 150…….(2)
3. Adding equations (1) and (2), we have 3l = 150, i.e. l = 50
a. Putting the value of l in equation (2), we have 5s = 150 + 150, i.e. s = 60
4. Hence, initial books in the library = l + s = 50 + 60 = 110
Thus, the library initially had 110 books in total.
Answer : B
Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren’s score, whose
score was 1/5^{th} more than Cook’s score. Eoin scored more than Cook and Darren’s score was 3/2 times that of Bell’s score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?
Given:
To Find: Range of the scores of the group
Approach:
Working out:
4. Bell’s Score
5. Eoin’s Score
6. Also, sum of all the scores = 250
So, the range of the scores of the group is 40.
Answer D
In triangle ABC, ∠ABC is 7/20 times less than ∠ACB, and ∠ACB is 2/3 times greater than ∠BAC. What is the measure of ∠BAC?
Given:
To Find:
a^{o} = ?
Approach:
Working out:
Looking at the answer choices, we see that the correct answer is Option B
The students in a class were asked to vote for their favourite subject. W students voted for mathematics, X students voted for science, Y for history and Z for literature. The ratio of W to Y was 4:5, Z to W was 5:6 and X to Z was 13:10. If each student in the class voted for one of the four subjects above, what percent of the students in the class voted for mathematics?
Given:
To Find: % of students who voted for Mathematics as their favorite subject
Approach:
2. So, to find the required percentage, we need to find the values of
Working out:
Looking at the answer choices, we see that the correct answer is Option C
2/5more water by weight is added to a saltsugarwater solution. Before the addition of the water, what is the ratio of the weight of the water to the weight of the solution?
Step 1 & 2: Understand Question and Draw Inference
Given:
Initial Solution
Final Solution
Step 3 : Analyze Statement 1 independent
(1) Due to the addition of water, the ratio of the weight of sugar in the solution to the weight of the solution decreases from to
Initial Solution
Thus, Statement 1 is sufficient.
Step 4 : Analyze Statement 2 independent
(2) After the addition of water, the ratio of the weight of water in the solution to the weight of the solution becomes 7/10
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
A teacher took a preannounced test in a class 3/4^{th}. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3^{rd} passed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?
Given:
To Find: fraction of the students who had not prepared for the test and failed the test?
Approach:
Working out:
2. Number of students who failed the test = 75% of x = 3/4
3. Also, number of students who failed the test = Number of students who prepared and failed the test + Number of students who did not prepare and failed the test
Answer E
In a developing country, the price of a stock is directly proportional to the reciprocal of the inflation in the country, which is in turn directly proportional to the local diesel prices. The price of the stock is 100 currency units when the inflation is 10 units and when the inflation is 12 units, the local price of the diesel is 60 currency units. By how many currency units should the local diesel price fall so that the price of the stock, which is currently at 200 currency units, increases by 25 percent?
Given:
where x is a constant and P and I are price of the stock and Inflation respectively
To Find: By how many currency units should the local diesel price fall so that the price of the stock, which is currently at 200 currency units, increases by 25 percent?
Approach:
Working out:
2. Calculating values of x and b
which gives us x = 1000
4. So, the fall in local diesel price = 25 – 20 = 5
Hence, the local diesel price should fall by 5 currency units so that the price of
the stock should increase by 25% from 200.
Answer : A
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