Algebra - Simple Equations - Previous Year CAT/MBA Questions
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The minimum number of flowers with which Roopa leaves home is
- (a)
16
- (b)
15
- (c)
0
- (d)
Cannot be determined
Answer: Option B
Text Explanation :
Starting from the fourth place of worship and moving backwards, we find that number of flowers before
entering the first place of worship is
For y = 16, the value of
Hence, the minimum number of flowers with which Roopa leaves home is 15.
Workspace:
Directions: Answer the questions based on the following information.
Rajiv reaches city B from city A in 4 hours, driving at speed of 35 kmph for the first two hour and at 45 kmph for the next two hours. Aditi follows the same route, but drives at three different speeds: 30, 40 and 50 kmph, covering an equal distance in each speed segment. The two cars are similar with petrol consumption characteristics (km per litre) shown in the figure below.
The quantity of petrol consumed by Aditi for the journey is
- (a)
8.3 I
- (b)
8.6 I
- (c)
8.9 I
- (d)
9.2 I
Answer: Option C
Text Explanation :
Distance between A and B = (35 × 2) + (45 × 2) = 160 km.
Distance covered by Aditi in each speed segment
Hence, total petrol consumed
Workspace:
Zoheb would like to drive Aditi’s car over the same route from A to B and minimize the petrol consumption for the trip. What is the quantity of petrol required by him?
- (a)
6.67 l
- (b)
7 l
- (c)
6.33 l
- (d)
6.0 l
Answer: Option A
Text Explanation :
For minimum petrol consumption, Zoheb should drive at 40 kmph, petrol consumption = = 6.67 I.
Workspace:
Directions: Answer the questions based on the following information.
Recently, Ghosh Babu spent his winter vacation on Kyakya Island. During the vacation, he visited the local casino where he came across a new card game. Two players, using a normal deck of 52 playing cards, play this game. One player is called the ‘dealer’ and the other is called the ‘player’. First, the player picks a card at random from the deck. This is called the base card. The amount in rupees equal to the face value of the base card is called the base amount. The face values of ace, king, queen and jack are ten. For other cards the face value is the number on the card. Once the ‘player’ picks a card from the deck, the ‘dealer’ pays him the base amount. Then the ‘dealer’ picks a card from the deck and this card is called the top card. If the top card is of the same suit as the base card, the ‘player’ pays twice the base amount to the ‘dealer’. If the top card is of the same colour as the base card (but not the same suit), then the ‘player’ pays the base amount to the ‘dealer’. If the top card happens to be of a different colour than the base card, the ‘dealer’ pays the base amount to the ‘player’.
Ghosh Babu played the game four times. First time he picked eight of clubs and the ‘dealer’ picked queen of clubs. Second time, he picked ten of hearts and the ‘dealer’ picked two of spades. Next time, Ghosh Babu picked six of diamonds and the ‘dealer’ picked ace of hearts. Lastly, he picked eight of spades and the ‘dealer’ picked jack of spades. Answer the following questions based on these four games.
If Ghosh Babu stopped playing the game when his gain would be maximized, the gain in Rs. would have been
- (a)
12
- (b)
20
- (c)
16
- (d)
4
Answer: Option A
Text Explanation :
Hence, we see that the maximum gain is Rs. 12
Workspace:
The initial money Ghosh Babu had (before the beginning of the game sessions) was Rs. X. At no point did he have to borrow any money. What is the minimum possible value of X?
- (a)
16
- (b)
8
- (c)
100
- (d)
24
Answer: Option B
Text Explanation :
Since the maximum negative that Ghosh Babu goes into is –8, he should begin with at least Rs. 8, so that he does not have to borrow any money at any point.
Workspace:
If the final amount of money that Ghosh Babu had with him was Rs. 100, what was the initial amount he had with him?
- (a)
120
- (b)
8
- (c)
4
- (d)
96
Answer: Option D
Text Explanation :
From the above table it is evident that in four games, Ghosh Babu makes a profit of Rs. 4. Hence, if the final amount left with Ghosh Babu is Rs. 100, the initial amount that he had would be Rs. 96.
Workspace:
A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.
- (a)
Rs. 10
- (b)
Rs. 15
- (c)
Rs. 7.50
- (d)
Cannot be determined
Answer: Option A
Text Explanation :
Let the cost of the turban be T.
Total payment for one year = Rs. 90 + T. So the payment for 9 months should be (90 + T). But this is equal to (65 + T). Equating the two, we get T = Rs. 10.
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My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate cost Re 1. The cost of apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if number of chocolates, biscuits and apples brought were all integers?
- (a)
Rs. 34
- (b)
Rs. 33
- (c)
Rs. 8
- (d)
None of these
Answer: Option A
Text Explanation :
Let the number of chocolates be c.
Number of apples has to be more than 3c, lets say 3c + k, k is a positive integer.
Total spend = 8c + 2k
for c = 4, k = 2
Total spend = 34
Hence (a) is the answer.
The cost of each chocolate is Re 1. So the cost of apple should be Rs. 2 and that of one biscuit should be Re 0.5. Thus, if he eats x chocolates, he has to eat 2x biscuits. Hence, the total value of chocolates will be Rs. x and that of biscuits will be (0.5)(2x) = Rs. x. Hence, we see that the value of chocolates is to the value of biscuits will always be 1 : 1. As per our assumption he will have to eat more than (x + 2x) = 3x apples and hence the total value of the apples will be more than (2)(3x) = 6x. In other words, the ratio of value chocolates to apples or biscuits to apples will be more than 1 : 6. In other words, if the value of chocolates and biscuits is Re 1 each, then the value of apples has to be more than Rs. 6, or the combined value will be more than Rs. 8. This means that the
value of apples will always constitute more than or of the entire bill. It can further be observed that the total value of chocolates and biscuits together will always be an even integer and so will be the value of apples. This means that the combined value of all three of them has to be even and not odd. So Rs. 33 cannot be the answer. Also Rs. 8 cannot be the answer as, if we take the value of chocolates and biscuits to be minimum, i.e. Re 1 each, then the value of apples can be a minimum of Rs. 8. Hence, the total value will always be Rs. 10 or higher. The only option possible is Rs. 34. To verify this let us find two even numbers (one of them higher than of 34) which adds 34.
We can find many such numbers e.g. 32 + 2, 30 + 4, 28 + 6 and 26 + 8. All of these could be a possible combination.
Workspace:
Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as
1. if the question can be answered with the help of any one statement alone but not by the other statement.
2. if the question can be answered with the help of either of the statements taken individually.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.
What is the price of tea?
I. Price of coffee is Rs. 5 more than that of tea.
II. Price of coffee is Rs. 5 less than the price of a cold drink which cost three times the price of tea.
Answer: 3
Text Explanation :
From the statement II, we can frame the equation that:
(Cold drink) = 3(Tea) and (Coffee) = (Cold drink) – 5 = 3(Tea) – 5. So we have one equation in terms of prices of tea and coffee. Although, this alone may not be sufficient to answer the question, in the light of the equation provided by the first statement, viz. (Coffee) = (Tea) + 5, we can solve the two equations simultaneously and get the price of tea.
Workspace:
Once I had been to the post office to buy five-rupee, two-rupee and one-rupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more one-rupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought?
- (a)
10
- (b)
9
- (c)
12
- (d)
8
Answer: Option A
Text Explanation :
Since I paid Rs. 20 and because of lack of change, the clerk gave me Rs. 3 worth of stamps, it can be concluded that the total value of the stamp that I wanted to buy is Rs. 17. Since I ordered initially a minimum of 2 stamps of each denominations, if I buy exactly 2 stamps each, my total value is 2(5 + 2 + 1) = Rs. 16. The only way in which I make it Rs. 17 is buying one more stamp of Re 1. Hence, the total number of stamps that I ordered = (2 + 2 + 3) = 7. In addition, the clerk gave me 3 more.
Hence, the total number of stamps that I bought = (7 + 3) = 10 (viz. 2 five-rupee, 2 two-rupee and 6 one-rupee stamps).
Workspace:
Direction: Answer the questions based on the following information.
A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.
What is the actual price per piece?
- (a)
Rs. 82
- (b)
Rs. 41
- (c)
Rs. 6
- (d)
Rs. 28
Answer: Option B
Text Explanation :
Hint: Students, please note that this sum could be intelligently solved by looking at both the questions together and also the answer choices. We know that the inventory has reduced by 54 units. This means two things: (i) actual quantity sold was less than the figure that was entered the computer (i.e. after interchanging digits), so the unit’s place digit of the actual quantity sold should be less than its ten’s place digit; and (ii) the difference between the actual quantity sold and the one that was entered in the computer is 54. From question 125, we can figure out that the only answer choice that supports both these conditions is (a), as (82 – 28 = 54). So the actual quantity sold = 28. Now since the total sales is Rs.1,148, actual price per piece = = Rs. 41.
Hence, the answer to question 124 is (b).
Workspace:
What is the actual quantity sold?
- (a)
28
- (b)
14
- (c)
82
- (d)
41
Answer: Option A
Text Explanation :
Hint: Students, please note that this sum could be intelligently solved by looking at both the questions together and also the answer choices. We know that the inventory has reduced by 54 units. This means two things: (i) actual quantity sold was less than the figure that was entered the computer (i.e. after interchanging digits), so the unit’s place digit of the actual quantity sold should be less than its ten’s place digit; and (ii) the difference between the actual quantity sold and the one that was entered in the computer is 54. From question 125, we can figure out that the only answer choice that supports both these conditions is (a), as (82 – 28 = 54). So the actual quantity sold = 28. Now since the total sales is Rs.1,148, actual price per piece = = Rs. 41.
Hence, the answer to question 124 is (b).
Workspace:
The points of intersection of three lines 2X + 3Y – 5 = 0, 5X – 7Y + 2 = 0 and 9X – 5Y – 4= 0
- (a)
form a triangle
- (b)
are on lines perpendicular to each other
- (c)
are on lines parallel to each other
- (d)
are coincident
Answer: Option D
Text Explanation :
The three lines can be expressed as and Therefore, the slopes of the three lines are and respectively. For any two lines to be perpendicular to each other, the product of their slopes = –1. We find that the product of none of the slopes is –1. For any two be parallel, their slopes should be the same. This is again not the case. And finally for the two lines to be intersecting at the same point, there should be one set of values of (X, Y) that should satisfy the equations of 3 lines. Solving the first two equations, we get X = 1 and Y = 1. If we substitute this in the third equation, we find that it also satisfies that equation. So the solution set (1, 1) satisfies all three equations, suggesting that the three lines intersect at the same point, viz. (1, 1). Hence, they are coincident.
Workspace:
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
How many rupees did Suvarna start with?
- (a)
Rs. 60
- (b)
Rs. 34
- (c)
Rs. 66
- (d)
Rs. 28
Answer: Option C
Text Explanation :
Please note that the best way to solve this question is by working backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is Vibha who lost in this round, all the remaining three must have doubled their share.
In other words, they would have had Rs.16 each after the 3rd round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48 overall which comes from Vibha's share, her share before the 4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following table.
Suvarna started with Rs.66.
Workspace:
Who started with the lowest amount?
- (a)
Suvarna
- (b)
Tara
- (c)
Uma
- (d)
Vibha
Answer: Option D
Text Explanation :
Please note that the best way to solve this question is by working backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is Vibha who lost in this round, all the remaining three must have doubled their share.
In other words, they would have had Rs.16 each after the 3rd round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48 overall which comes from Vibha's share, her share before the 4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following table.
It was Vibha who started with the lowest amount, viz. Rs.10.
Workspace:
Who started with the highest amount?
- (a)
Suvarna
- (b)
Tara
- (c)
Uma
- (d)
Vibha
Answer: Option A
Text Explanation :
Please note that the best way to solve this question is by working backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is Vibha who lost in this round, all the remaining three must have doubled their share.
In other words, they would have had Rs.16 each after the 3rd round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48 overall which comes from Vibha's share, her share before the 4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following table.
It was Suvarna who started with the highest amount, viz. Rs.66.
Workspace:
What was the amount with Uma at the end of the second round?
- (a)
36
- (b)
72
- (c)
16
- (d)
None of these
Answer: Option B
Text Explanation :
Please note that the best way to solve this question is by working backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is Vibha who lost in this round, all the remaining three must have doubled their share.
In other words, they would have had Rs.16 each after the 3rd round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48 overall which comes from Vibha's share, her share before the 4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following table.
At the end of the second round, Uma had Rs.72.
Workspace:
Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, then the third number is
- (a)
10
- (b)
14
- (c)
16
- (d)
12
Answer: Option B
Text Explanation :
If the numbers are (x – 2), x and (x + 2), then 3(x – 2) – 2 = 2(x + 2).
∴ x + 2 = 14.
Workspace:
Answer the next 3 questions based on the information given below:
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
What was the worth of the total property?
- (a)
Rs. 30 lakh
- (b)
Rs. 8 lakh
- (c)
Rs. 18 lakh
- (d)
Rs. 24 lakh
Answer: Option D
Text Explanation :
Let us assume that Alphonso’s total property was of Rs.x.
Since Alphonso’s wife is also the mother of Dave, the total share of this lady would be
And since, = 1,575000
⇒ x = Rs.24 lakhs.
Workspace:
What was Carl’s original share?
- (a)
Rs. 4 lakh
- (b)
Rs. 12 lakh
- (c)
Rs. 6 lakh
- (d)
Rs. 5 lakh
Answer: Option A
Text Explanation :
Let us assume that Alphonso’s total property was of Rs.x.
Carl’s original share was = Rs. 4 lakhs.
Workspace:
What was the ratio of the property owned by the widows of the three sons, in the end?
- (a)
7 : 9 : 13
- (b)
8 : 10 : 15
- (c)
5 : 7 : 9
- (d)
9 : 12 : 13
Answer: Option B
Text Explanation :
Let us assume that Alphonso’s total property was of Rs.x.
The ratio’s of the property owned by the widows of the 3 sons = = 8 : 10 : 15.
Workspace:
Data is provided followed by two statements – I and II – both resulting in a value, say I and II.
As your answer,
Type 1, if I > II.
Type 2, if I < II.
Type 3, if I = II.
Type 4, if nothing can be said.
Nineteen years from now Jackson will be 3 times as old as Joseph is now. Johnson is three years younger than Jackson.
I. Johnson’s age now.
II. Joseph’s age now.
Answer: 4
Text Explanation :
Since the ages of none of them is mentioned and we have two equations and three unknowns.
Hence, we cannot say anything about the ages of any of them.
Workspace:
Data is provided followed by two statements – I and II – both resulting in a value, say I and II.
As your answer,
Type 1, if I > II.
Type 2, if I < II.
Type 3, if I = II.
Type 4, if nothing can be said.
Last week Martin received $ 10 in commission for selling 100 copies of a magazine. Last week Miguel sold 100 copies of this magazine. He received his salary of $ 5 per week plus a commission of 2 cents for each of the first 25 copies sold, 3 cents for each of next 25 copies sold and 4 cents for each copy thereafter. ($1 = 100 cents).
I. Martin’s commission in the last week.
II. Miguel’s total income for last week.
Answer: 1
Text Explanation :
Miguel’s income = 5 + (0.02 × 25) + (0.03 × 25) + (0.04 × 50) = $8.25.
Martin’s commission = $10.
Hence obviously I > II.
Workspace:
Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?
- (a)
Rs. 10
- (b)
Rs. 8
- (c)
Rs. 15
- (d)
Cannot be determined
Answer: Option C
Text Explanation :
The two equations are : 2o + 3b + 4a = 15 and 3o + 2b + a = 10.
Adding the two equations, we get
5o + 5b + 5a = 25
⇒ o + b + a = 5
∴ 3o + 3b + 3a = 15.
Hence, option (c).
Workspace:
Use the following information:
Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
How many children did not try any of the rides?
- (a)
5
- (b)
10
- (c)
15
- (d)
20
Answer: Option C
Text Explanation :
Let x, y and z be the number of children who took 1 rides, 2 rides and 3 rides respectively.
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who did not try any of the rides
= 85 – (x + y + z)
= 85 – (15 + 35 + 20) = 15
Hence, option (c).
Workspace:
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