Jasmine Grover Content Strategy Manager
Content Strategy Manager
Line Graph based Data Interpretation are simple to solve. Correct Approximation of value and comparison between two graphs and their nature is one of their questions. Questions from this topic is always asked in the CAT, XAT, GMAT, NMAT, CMAT, XGMT, TISSNET, MAT and many state level and central level entrance exams.
To understand the graphs and correctly measure the values from the graphs for calculations students should directly dive into questions and increase their muscle memory.
Topics to be discussed in this article are:-
- Previous year CAT questions on Graphs.
- How to approach questions on Graphs in CAT exam.
Previous year CAT questions on Line Graphs
Directions (Q. Nos. 1-4) Refer to the following chart and solve the questions based on it. (CAT 2016)
The figure below represents the sales and net profit (in Rs. crore) of IVP Ltd. for five years from 2010-11 to 2014-15. During this period, the sales increased from Rs.100 crore to Rs.680 crore. Correspondingly, the net profit increased from Rs. 2.5 crore to Rs. 12 crore. (Net profit is defined as the excess of sales over total costs)
Ques 1. The highest percentage growth in sales, relative to the previous year occurred in
(a) 2011-12 (b) 2012-13 (c) 2013-14 (d) 2014-15
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Solution:- (a)
| Year | Previous sales | Current sales | Difference | Percentage |
|---|---|---|---|---|
| 2011-12 | 100 | 250 | 150 | 150% |
| 2012-13 | 250 | 300 | 50 | 20% |
| 2013-14 | 300 | 290 | -10 | -3.33% |
| 2014-15 | 290 | 680 | 390 | 134.5% |
the maximum percentage increase relative to previous year occurred in 2011-12.
Ques 2. The highest percentage growth in net profit, relative to the previous year, was achieved in
(a) 2014-15 (b) 2013-14 (c) 2012-13 (d) 2011-12
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Solution:- (b)
| Year | Previous profit | Current profit | Difference | Percentage |
|---|---|---|---|---|
| 2011-12 | 2.5 | 4.5 | 2 | 80% |
| 2012-13 | 4.5 | 6 | 1.5 | 33.33% |
| 2013-14 | 6 | 8.5 | 2.5 | 41.66% |
| 2014-15 | 8.5 | 12 | 3.5 | 41.2% |
the highest percentage growth in net profit relative to the previous year was achieved in 2013-14.
Ques 3. Defining profitability as the ratio of net profit to sales, IVP Ltd. recorded the highest profitability in
(a) 2014-15 (b) 2013-14 (c) 2010-11 (d) 2012-13
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Solution:- (b)
| Years | Net profit | Net sales | Ratio |
|---|---|---|---|
| 2010-11 | 2.5 | 100 | 0.025 |
| 2011-12 | 4.5 | 250 | 0.02 |
| 2012-13 | 6 | 300 | 0.02 |
| 2013-14 | 8.5 | 290 | 0.03 |
| 2014-15 | 12 | 680 | 0.018 |
the maximum is in profitability 2013-14.
Ques 4. With profitability as defined in question 7, it can be concluded that
(a) Profitability is non-decreasing during the five years from 2010-11 to 2014-15
(b) Profitability is non-increasing during the five years from 2010-11 to 2014-15
(c) Profitability remains constant during the five years from 2010-11 to 2014-15
(d) None of the above
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Solution:- (d)
Profitability doesn't have a set pattern, and the first three lines try to explain it in a general way.
So, they don't apply, and answer choice (d) is the right one.
Directions (Q. Nos. 5-6) Go through the chart below and answer the questions based on it. (CAT 2015)
Valuation of currencies
Above given four currencies represents the following
US Dollar, Singapore Dollar, UK Pound and Euro Following is the order of their valuations UK Pound > US Dollar > Euro > Singapore Dollar
Ques 5. A person wants to buy an article worth 65 Singapore Dollars. If Singapore Dollar loses 2% with respect to the above given exchange rates, then how many US dollars must be spend? _______ US dollars.
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Solution:-
Taking into account the above rates:
1 US Dollar = Rs.45.94 and
1 Singapore Dollar = Rs.30.27
Hence, 1 US Dollar = 1.52 Singapore Dollar
The Singapore Dollar has declined by 2% relative to the above exchange rates.
So, 1 US Dollar = 1.52 × 1.02 = 1.55 Singapore Dollar.
Thus, 65 Singapore Dollar equals 41.9 U.S.
Therefore, the individual must pay 41.9 US Dollar to receive 65 Singapore Dollar.
Ques 6. A person wants to buy 800 barrels of oil. The payment can be made either in US Dollars or in Euros. If the payment is made in Euros, then it would be 47 Euros per barrel while if one pays in US Dollars, the rate would be 29 US Dollars per barrel. How much money will he save, if he goes for the cheaper deal?_______ US Dollars.
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Solution:-
Price for 800 barrels = 37600 Euros = Rs.1253960
However, if we pay in U.S. dollars, we will pay 23200 dollars, which is equivalent to 1065808 dollars. Consequently, we pay Rs.188152 less = 4096 US Dollar
Directions (Q. Nos. 7-10) Answer the questions based on the following two graphs, assuming that there is no fixed cost component and all the units produced are sold in the same year.(CAT 2014)
Ques 7. In which year per unit cost is highest?
(a) 2002 (b) 2001 (c) 2005 (d) 2007
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Solution:- (b)
Suppose x units are produced each year.
In the year 2002,
Total revenue = 1200
⇒ 12 × x = 1200
⇒ x=100
Profit = 300
∴Cost price = 1200 − 300 = 900
Cost per unit is 9
In the year 2001,
Total revenue = 1400
⇒ 14 × x = 1400
⇒ x = 100
Profit = 100
∴Cost price = 1400 − 100 = 1300.
Ques 8. What is the approximate average quantity sold during the period 2000-2010?
(a) 64 units (b) 70 units (c) 77 units (d) 81 units
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Solution:- (b)
| Year | Unit price | Revenue | Total units = Revenue /Unit price |
|---|---|---|---|
| 2000 | 10 | 700 | 70 |
| 2001 | 14 | 1400 | 100 |
| 2002 | 12 | 1200 | 100 |
| 2003 | 12 | 900 | 75 |
| 2004 | 11 | 1100 | 100 |
| 2005 | 8 | 400 | 50 |
| 2006 | 10 | 200 | 20 |
| 2007 | 14 | 700 | 50 |
| 2008 | 10 | 600 | 60 |
| 2009 | 10 | 800 | 80 |
| 2010 | 15 | 900 | 60 |
| Total | 765 |
Ques 9. If the price per unit decrease by 20% during 2000-2004 and cost per unit increase by 20% during 2005-2010, then during how many number of years there is a loss?
(a) 3 yr (b) 4 yr (c) 5 yr (d) 7 yr
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Solution:- (c)
| Years | New Revenue | Total cost =. Old Revenue- Profit |
|---|---|---|
| 2000 | 80% of 700 =560 | 700 |
| 2001 | 80% of 1400=1120 | 1300 |
| 2002 | 80% of 1200=960 | 900 |
| 2003 | 80% of 900=720 | 750 |
| 2004 | 80% of 1100=880 | 1100 |
| 2005 | 400 | 120% of 250=300 |
| 2006 | 200 | 120% of 100=120 |
| 2007 | 700 | 120% of 500=600 |
| 2008 | 600 | 120% of 600=720 |
| 2009 | 800 | 120% of 400=480 |
| 2010 | 900 | 120% of 600=720 |
The years 2000, 2001, 2003, 2004 and 2008 (5 years total) when there is a loss (Total cost > Revenue)
Ques 10. If volatility of a variable during 2000-2010 is defined as (Maximum value − Minimum value)/ Average value , then which of the following is true?
(a) Price per unit has highest volatility (b) Cost per unit has highest volatility (c) Total profit has highest volatility (d) Revenue has highest volatility
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Solution:- (c)
Using trial and error with options.
Option (a) - Volatility per unit = (15-8)/(126/11) = 77/126 = 0.611
Option (b),
Total cost = Revenue – Profit
= (700 + 1400 + 1200 + 900 + 1100 + 400 + 200 + 700+600+800+900) − (0+100+300+150) + 0 + 150 + 100 + 200 + 0 + 400 + 300) = 8900 − 1700 = 7200
Volatility per unit = \(\frac{(1400-100)-(200-100)}{7200} = \frac{1300-100}{7200}\) x 11 = 1.833
Option (c)
Average Profit = 1700/11
Profit volatility = (400-0)/(1700/11) = 2.588
Option (d)
Average revenue = 8600/11
Revenue Volatility = (1400-200)/(8600/11) = 1.535
Highest volatility has total profit. So, Option (c)
Directions (Q. Nos. 11-15) Refer to the following graph and answer the questions. (CAT 2010)
Ques 11. Which month has the highest profit per employee?
(a) September (b) July
(c) January (d) March
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Solution:- (d)
In May, the number of employees abruptly increases, while profits increase at a much slower rate; therefore, the highest profit per employee must have occurred in either January or March, based on a comparison of the values for the graph. March is the month that is accurate.
Ques 12. Which month records the highest profit
(a) September (b) July
(c) March (d) May
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Solution:- (a)
Profit = (Sales - Cost)
Since September is when the difference between the sales and cost line graphs is greatest, this is the correct answer.
Ques 13. In which month is the percentage increases in sales over the sales two months before, the highest?
(a) March (b) September
(c) July (d) May
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Solution:- (a)
Comparing the value of sales in different months based on the conditions, the largest difference is between January and March, while the smallest difference is between January and the base value; therefore, the largest percentage increase will occur in March.
Ques 14. In which month is the total increase in the cost highest as compared to the cost two months ago?
(a) March (b) September
(c) July (d) May
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Solution:- (d)
Ques 15. Assuming that no employee left the job, how many more people did the company take on in the given period?
(a) 4600 (b) 5100
(c) 5800 (d) 6400
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Solution:- (b)
How to approach questions on Graphs in CAT exam
- One should know how to read two axis simultaneously and compare with other points on the graphs.
- Student should know the trend of line graphs for faster interpretation and calculation.
- At times, tabulation graph of complex questions will yield faster results.
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