Is Data Interpretation Basics important for XAT?

Yes, a solid understanding of Data Interpretation Basics is essential for performing well in the XAT DILR section. These foundational concepts underpin all DI sets and are required for accurate and fast data analysis.

What does Data Interpretation Basics cover in XAT?

Data Interpretation Basics in XAT covers fundamental skills such as reading tables, understanding ratios and percentages, calculating averages and totals from raw data, identifying trends, and interpreting simple graphs and charts correctly.

How can I prepare for Data Interpretation Basics in XAT?

Candidates should strengthen their understanding of percentages, ratios, averages, and basic arithmetic. Practise reading simple data tables and graphs and answering calculation-based questions accurately. Building speed in basic calculations is crucial for DI performance in XAT.

Are Data Interpretation Basics questions difficult in XAT?

Data Interpretation Basics questions are generally of easy to moderate difficulty. However, accuracy and speed are critical, as errors in basic calculations can affect the entire set of related questions.

How do Cracku's XAT Data Interpretation Basics questions help in preparation?

Cracku's XAT Data Interpretation Basics questions provide foundational practice with clear, step-by-step solutions. They help candidates build confidence in core DI skills before progressing to more complex and multi-level data interpretation sets in the XAT exam.

XAT Data Interpretation Basics Questions

Instructions

Study the data given in the table below and answer the question that follow:

All figures are in percentage
Based on survey of ‘shop types’ Kamath categorized Indian states into four geographical regions as shown in the table above. His boss felt that the categorization was inadequate since important labels were missing. Kamath argued that no further labels are required to interpret the data.

Question 1

A consultant observing the data made the following two inferences:
Inference I: The number of Grocers per-thousand-population is the highest in North India.
Inference II: The number of Cosmetic per-thousand-population is the highest in South India.

Which of following options is DEFINITELY correct?

Inference I alone is correct.

Inference II alone is correct.

Either of the inferences is correct.

Neither of the inference is correct.

Inference I will be correct only if inference II is correct.

Question 2

The average size of Food Shops in East India was twice that of Food Shops in West India. Which of the following cannot be inferred from the above data?

As far as ‘Food Shops’ are concerned, customers in East India prefer spatial surroundings compared to customers in the West India.

As far as ‘Food Shops’ are concerned, Rentals are very high in West India compared to East India.

The ratio of customers buying from ‘Food Shops’ in East India to customers buying from ‘Food Shops’ in West India is 15.8 : 11.8.

There are740 ‘Food Shops’ in West India.

There are 240 ‘Food Shops’ in South India.

Question 3

Bala collected the same data five years after Kamath, using the same categorization.

Which of the following statements can DEFINITELY be concluded?

In the last four years the number of Electrical hardware shop types has increased in North India.

In the last four years the number of Grocers shop types has increased in South India.

For the last four years in All India the number of Chemists shop types has remained constant.

In the four years in East India the number of ‘other’ shop type has decreased.

As per the new survey conducted Pan Bidi shops in East India are next only to Grocers.

Instructions

Based on the following information

Total income tax payable is obtained by adding two additional surcharges on calculated income tax.

Education Cess : An additional surcharge called ‘Education Cess’ is levied at the rate of 2% on the amount of income tax.

Secondary and Higher Education Cess : An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.

Question 1

Sangeeta is a young working lady. Towards the end of the financial year 2009 - 10, she found her total annual income to be Rs. 3, 37, 425/ -. What % of her income is payable as income tax?

5.64

6.82

7.38

8.10

None of the above

Video Solution

Question 2

Mr. Madan observed his tax deduction at source, done by his employer, as Rs. 3,17,910/-. What was his total income (in Rs.) if he neither has to pay any additional tax nor is eligible for any refund?

13,48,835/-

14,45,522/-

14,47,169/-

15,70,718/-

None of the above

Video Solution

Instructions

Answer questions based on the following information:
Mulchand Textiles produces a single product of only one quality – waterproof synthetic fabric. Mr.Sharma, the cost accountant of Mulchand Textiles, estimated the costs of Mulchand Textiles for different possible monthly output levels. Before he could tabulate his estimates his computer crashed, and Mr. Sharma lost all data. Fortunately he had some printouts of some incomplete tables, charts and diagrams. The table titled “Variable Cost Estimates of Mulchand Textiles” provided the estimates of labour and material costs.

Apart from labour and material costs Mulchand Textiles incurs administrative costs of Rs. 40,000 per month, and electricity costs. Mr. Sharma recalled that estimate data of variable electricity cost had certain peculiar characteristics. Values at every 25000 sq ft of output increased in geometric progression till 150000 sq ft of output, after which values increased in arithmetic progression for every 25000 sq ft of output. Mr. Sharma remembered that the electricity cost was estimated to be Rs. 3800 for 25000 sq.ft. of output, Rs. 5700 for 50000 square feet of output and Rs. 38856.50 for 175000 square feet of output.

Question 3

The estimated cost per square feet of output is least for:

75000 square feet output

100000 square feet output

125000 square feet output

150000 square feet output

175000 square feet output

Question 4

The estimated material cost given in the table titled “Variable Cost Estimates of Mulchand Textiles” included the cost of material that gets spoiled in the production process. Mr. Sharma decomposed the estimated material cost into material spoilage cost and material usage cost, but he lost the data when his computer crashed. When he saw the following line diagram, here called that he measured the estimate of material spoilage cost per square feet of output on the y - axis and monthly output on the x - axis.

Estimated material usage cost per square feet of output.

Decreases up to 125000 square feet of monthly output and then increases monotonically.

Decreases up to 50000 square feet of monthly output, remains constant between 50000 and l00000, decreases between 100000 and 125000, remains constant between 125000 and 175000 and finally increases between 175000 and 200000 of monthly output.

Remains constant for all levels of monthly output.

Increases up to 50000 square feet of monthly output, remains constant between 50000 and l00000, increases between 100000 and 125000, remain constant between 125000 and 175000 and finally decreases between 175000 and 200000 of monthly output.

Increases up to 100000 square feet of monthly output and then decreases monotonically.

Question 5

Mr. Sharma found some printouts of line diagrams. The axes of the graphs were not marked, but Mr. Sharma remembered that he measured monthly output on the x - axis. Which of the following diagrams would represent the estimates of electricity cost per square feet of output versus monthly output?

Solution

It is given that cost for electricity changed in geometric progression till 150000 sq ft.

Estimated electricity cost for 25000 sq. ft = Rs. 3800

Estimated electricity cost for 50000 sq. ft = Rs. 5700

Hence, we can say that common ratio of the GP that is formed by electricity cost = $$\dfrac{5700}{3800}$$ = 1.5

Therefore, estimated electricity cost for 75000 sq. ft = 5700*1.5 = Rs. 8550.

Similarly, we can calculate the electricity cost till 150000 sq. ft.

Estimated electricity cost for 200000 sq. ft = 2*Estimated electricity cost for 175000 sq. ft - Estimated electricity cost for 150000 sq. ft = 2*38856.5 - 28856.25 = Rs. 48856.75 {As these numbers are in an arithmetic sequence).

Electricity cost per sq. ft. for 25000 sq. ft = $$\dfrac{3800}{25000}$$ = Rs. 15

Similarly, we can calculate the remaining data.Tabulating the all data,

We can see from the table that the cost per sq. ft decreased first then increased to 0.24 which is present in option B. Hence, option B is the correct answer.

Instructions

answer questions based on the following information:

In the beginning of the year 2010, Mr. Sanyal had the option to invest Rs. 800000 in one or more of the following assets – gold, silver, US bonds, EU bonds, UK bonds and Japanese bonds. In order to invest in US bonds, one must first convert his investible fund into US Dollars at the ongoing exchange rate. Similarly, if one wants to invest in EU bonds or UK bonds or Japanese bonds one must first convert his investible fund into Euro, British Pounds and Japanese Yen respectively at the ongoing exchange rates. Transactions were allowed only in the beginning of every month. Bullion prices and exchange rates were fixed at the beginning of every
month and remained unchanged throughout the month. Refer to the table titled “Bullion Prices and Exchange Rates in 2010" for the relevant data.
Bullion Prices and Exchange Rates in 2010

Interest rates on US, EU, UK and Japanese bonds are 10%, 20%, 15% and 5% respectively.

Question 6

Mr. Sanyal adopted the following investment strategy. On lst January 2010 he invested half of his investible fund in gold and the other half he kept in fixed deposit of an Indian bank that offered 25% interest per annum. At the beginning of every quarter he liquefied his assets to create his investible fund for that quarter. Every quarter he invested half of his fund in the bullion that gave maximum return in the previous quarter and the other half in the foreign bond that gave maximum return in the previous quarter. However, if in any quarter none of the foreign bonds gave a better return than the fixed deposit of his Indian bank, he invested half of his investible fund in the fixed deposit for the next quarter. On 31st December 2010 Mr. Sanyal liquefied his assets and realized that all of the following options are true except:

By investing the entire amount in US bonds, he would have gained an additional Rs. 118395.

By investing the entire amount in UK bonds, he would have gained an additional Rs. 65035.

By investing the entire amount in EU bonds, he would have gained an additional Rs. 65035.

By investing the entire amount in Japanese bonds, he would have gained an additional Rs. 38395.

By investing the entire amount in fixed deposit of his Indian bank he would have gained an additional Rs.38395.

Question 7

Advisors were asked to prepare an investment strategy that involved US Bonds, EU Bonds and Japanese Bonds, keeping at least 20% of the initial fund in each of these assets for the entire year, and allowing exactly four additional transactions in the course of the year. On 2nd January 2011, while comparing five different recommendations that he had received from his financial advisors in the beginning of 2010, Mr. Sanyal referred to the table “Bullion Prices and Exchange Rates in 20
10”. One transaction is defined as the buying or selling of an asset. Which of the recommendation out of the following was the best one?

Two additional transactions each during the month of June and November.

Two additional transactions each during the month of June and October.

Two additional transactions each during the month of May and June.

Two additional transactions each during the month of March and November.

Two additional transactions each during the month of March and October.

Solution

To determine the best investment strategy for Mr. Sanyal, we must identify the timing that maximizes returns from two sources: the annual interest rates of the bonds (EU at 20%, US at 10%, and Japan at 5%) and the exchange rate appreciation of the respective currencies against the Rupee (Rs.). Since the rules require at least 20% of the initial Rs. 800,000 to remain in each asset for the entire year, the goal is to move the "flexible" remainder of the funds into the asset that is about to experience the steepest growth in value.

The most significant variable in this scenario is the US Dollar (US$), which starts the year at Rs. 40 and ends at Rs. 50, representing a 25% appreciation. However, this growth is not linear. Between April and June, the exchange rate is completely stagnant at Rs. 42. It then begins a sharp climb starting in July, hitting Rs. 44, and continues rising until it peaks and stabilizes at Rs. 50 in November and December.

By choosing Option A (June and November), the investor perfectly brackets this growth period. Shifting the flexible capital in June allows the investor to buy into US bonds just before the currency begins its rapid ascent from 42 to 50. Conversely, performing transactions in March or May would be premature, as the capital would sit in a stagnant currency while missing out on the superior 20% interest rate offered by the EU bonds during those months.

Finally, the November transaction allows the investor to "lock in" the gains from the US Dollar's peak. Since the exchange rate remains at 50 through December, there is no further currency gain to be had in the final month. By moving funds in November, the investor can shift back into the higher-interest EU bonds for the final month of the year, ensuring the highest possible closing balance for the portfolio.
Thus, the correct answer is Option A.

Question 8

Mr. Sanyal invested his entire fund in gold, US bonds and EU bonds in January 2010. He liquefied his assets on 31st August 2010 and gained 13% on his investments. If instead he had held his assets for an additional month he would have gained 16.25%. Which of the following options is correct?

Mr. Sanyal invested less than 40% in gold and more than 40% in EU bonds.

Mr. Sanyal invested less than 40% in each of gold and US bonds.

Mr. Sanyal invested less than 40% in gold, and less than 25% in US bonds.

Mr. Sanyal invested more than 40% in gold, less than 25% in EU bonds.

Mr. Sanyal invested more than 40% in each of US bonds and EU bonds.

Solution

If you go through the options, you will find that only option B supports the given conditions.

Let the ratio of investments in gold, US and EU bonds be 40%, 40% and 20%, respectively.

Thus, the investment amounts are 320000, 320000 and 160000, respectively.

For returns in August 2010:

Gold: (20720/20000) *320000 = 331520

US bonds: (45/40)*320000 + (320000 * 8 * 10)/(12 * 100) = 381333

EU bonds: (63/60)*160000 + (160000 * 8 * 20)/(12 * 100) = 189333

Thus, total returns in August = 902186

Thus, percentage return = 90218600/800000 = 13 ( approx.)

Hence, it satisfies the condition for August.

For returns in September 2010:

Gold: (20850/20000) *320000 = 333600

US bonds: (47/40)*320000 + (320000 * 9 * 10)/(12 * 100) = 400000

EU bonds: (64/60)*160000 + (160000 * 9 * 20)/(12 * 100) = 194666

Thus, total returns in August = 928266

Thus, percentage return = 92826600/800000 = 16.25 ( approx.)

Hence, it satisfies the condition for September, too.

Hence, option B is the answer.

Question 9

At the beginning of every month, by sheer luck, Mr. Sanyal managed to correctly guess the asset that gave maximum return during that month and invested accordingly. If he liquefied his assets on 31st December 2010, how much was the percentage gain from his investments?

34.64%

46.71%

47.5%

49.15%

49.96%

Solution

To solve this problem, we need to find the maximum possible return Mr. Sanyal could achieve by shifting his entire capital (Rs. 800,000) into the single best-performing asset at the beginning of every month. Each month, the "return" is a combination of that month's accrued interest and the percentage change in the asset's price (bullion) or exchange rate (bonds).
Each monthly multiplier is calculated as the maximum of:
Bullion Yield: $$\frac{\Pr ice\ at\ the\ end\ of\ month}{\Pr ice\ at\ the\ start\ of\ month}$$
Bond Yield:$$\frac{Exchange\ rate\ at\ the\ end\ of\ month}{Exchange\ rate\ at\ the\ start\ of\ month}\times\ \left(1+\frac{Annual\ interest\ rate\ }{12}\right)$$.

Jan: EU Bond -> 1 + (61.5/60 - 1) + 0.20/12 = 1.04167
Feb: EU Bond -> 1 + (62/61.5 - 1) + 0.20/12 = 1.02480
Mar: US Bond -> 1 + (41/41 - 1) + 0.10/12 = 1.00833 (Gold/Silver actually lower)
Apr: UK Bond -> 1 + (72/71 - 1) + 0.15/12 = 1.02658
May: JP Bond -> 1 + (0.54/0.53 - 1) + 0.05/12 = 1.02302
Jun: US Bond -> 1 + (44/42 - 1) + 0.10/12 = 1.05595
Jul: US Bond -> 1 + (45/44 - 1) + 0.10/12 = 1.03106
Aug: US Bond -> 1 + (47/45 - 1) + 0.10/12 = 1.05278
Sep: US Bond -> 1 + (49/47 - 1) + 0.10/12 = 1.05089
Oct: US Bond -> 1 + (50/49 - 1) + 0.10/12 = 1.02874
Nov: JP Bond -> 1 + (0.60/0.59 - 1) + 0.05/12 = 1.02112
Dec: EU Bond (Interest only) -> 1 + 0 + 0.20/12 = 1.01667

1.04167×1.02480×1.00833×1.02658×1.02302×1.05595×1.03106×1.05278×1.05089×1.02874×1.02112×1.01667 $$\approx\ $$ 1.4671.
This amounts to an overall gain of 46.71%

Instructions

Answer questions based on the following information:

An automobiles company’s annual sales of its small cars depends on the state of the economy as well as on whether the company uses some high profile individual as its brand ambassador in advertisements of its product. The state of the economy is “good”, “okay” and “bad” with probabilities 0.3, 0.4 and 0.3 respectively. The company may choose a high profile individual as its brand ambassador in TV ads or may go for the TV ads without a high profile brand ambassador.

If the company fixes price at Rs. 3.5 lakh, the annual sales of its small cars for different states of the economy and for different kinds of TV ads are summarized in table 1. The figures in the first row are annual sales of the small cars when the company uses a high profile individual as its brand ambassador in its TV ads and the ones in the second row are that when the company does not use any brand ambassador in TV ads, for different states of the economy.
Table 1:

Without knowing what exactly will be the state of the company in the coming one year, the company will either have to sign a TV ad contract with some high profile individual, who will be the company’s brand ambassador for its small car for the next one year, or go for a TV ad without featuring any high profile individual. It incurs a cost of Rs. 3.45 lakh (excluding the payment to the brand ambassador) to put a car on the road.

When the company’s profit is uncertain, the company makes decisions on basis of its expected profit. If the company can earn a profit xi with probability pi (the probability depends on the state of economy), then the expected profit of the company is $$\sum_1XiPi$$

Question 1

The maximum that the company can afford to pay its brand ambassador is

Rs. 10.0 crore

Rs. 10.6 crore

Rs. 10.8 crore

Rs. 12.0 crore

Rs. 16.4 crore

Question 2

Mr. Khan a popular film actor, agrees to sign the contract to become the company’s brand ambassador for Rs. 9 crore. The cost to the company of putting a car on the road also got escalated. The maximum escalation in cost of putting a car on the road, for which the company can afford to sign the contract with Mr.Khan is

Rs. 900

Rs. 967

Rs. 1250

Rs. 1267

Rs. 1333

Solution

Expected profit when brand ambassador is used = (3.5 - 3.45)[100000 × 0.3 + 80000 × 0.4 + 50000 × 0.3] lakh = 0.05lakh*77000= 3850 lakh

Expected profit when brand ambassador is not used = (3.5 - 3.45)[80000 × 0.3 + 50000 × 0.4 + 30000 × 0.3] lakh =0.05lakh*53000= 2650 lakh

Difference = (3850 - 2650) = 1200 lakh = 12 crore.

When profit is Rs.12.0 crores when Mr. Khan Advertises for the company.

Then profit is (12.0 - 9.0) = Rs.3 crore

No. of cars sold when Mr. khan advertises = [100000 × 0.3 + 80000 × 0.4 + 50000 × 0.3]= 77000

No. of cars sold when no popular actor is for advertisement= [80000 × 0.3 + 50000 × 0.4 + 30000 × 0.3]=53000

No of extra vehicles sold due to Mr. Khan= 24000

Suppose p is the amount escalated in cost of putting a car on the road,

24000p = 3,00,00,000

p = Rs1250

Had the cost not been increased, the company would have a extra profit of Rs. 1250 due to brand ambassador.

So, this the maximum escalation for which the company can afford signing contract with Mr. Khan.

Hence, option C is the correct answer.

Question 3

Mr. Khan a popular film actor, agrees to sign the contract to become the company’s brand ambassador for Rs. 9 crore. The cost to the company of putting a car on the road also got escalated by Rs. 1000. If the company signs the contract with Mr.Khan, its profit will

increase by Rs. 40 lakh

increase by Rs. 60 lakh

decrease by Rs. 20 lakh

decrease by Rs. 40 lakh

decrease by Rs. 50 lakh

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