CAT 2021 Quant Question:
A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
A. 150
B. 225
C. 175
D. 200
Answer:
Let the number of small shirts be ‘x’
then the number of large shirts becomes 64 - x.
Let the price of a small shirt be ‘y’
then the price of a large shirt becomes y + 50
Money spent on small shirts = xy = 1800
Money spent on large shirts = (64 - x) (y + 50) = 5000
(64 - x) (y + 50) = 5000
64y + 3200 - xy - 50x = 5000
64y + 3200 - 1800 - 50x = 5000
64y + 1400 - 50x = 5000
64y - 50x = 3600
32y - 25x = 3600
32y - 25(1800/y) = 3600
32y2 - 3600y - 25(1800) = 0
4y2 - 9(25)y - 25(9)(25) = 0
y = 75
Price of a small shirt = ‘y’ = 75
Price of a small shirt = ‘y + 50’ = 125
The price of a large shirt and a small shirt together, in INR = 75 + 125 = 200
The answer is 200
Choice D is the correct answer.
CAT 2021 Quant Question:
Consider a sequence of real numbers 
such that
If 
A. 4949
B. 4849
C. 4850
D. 4950
Answer:
Similarly we see that,
Hence, the answer is 4850
Choice C is the correct answer.
CAT 2021 Quant Question:
A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is
Answer:
Since the prices of the small and medium cups are in the ratio 2 : 5,
Let us assume the prices of the small, medium and large cups to be 2x, 5x and y.
We are given that the product of the three prices is 800.
Therefore, (2x)(5x)(y) = 800 —- (1)
If the price of the smallest and the medium cups are increased by 6, then the product becomes 3200
(2x + 6) (5x + 6) (y) = 3200 —- (2)
Dividing (2) by (1)
10 x(x - 2) + 6(x - 2) = 0
(10x + 6) (x - 2) = 0
x = 2 or x = -0.6
x can’t be negative and hence x = 2
WKT, (2x)(5x)(y) = 800
(4)(10)(y) = 800
y = 20
Therefore, the sum of the prices = 2x + 5x + y
= 2(2) + 5(2) + 20
= 4 + 10 + 20
= 34
The answer is '34’
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CAT 2021 Quant Question:
The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is
Answer:
|1 + mn| < |m + n| < 5
For two numbers ‘a’ and ‘b’,
|a| < |b| is equivalent to 
So, we can say that:
For the product to be negative, either one of the two terms has to be negative.
But they cannot simultaneously be 0.
The only possibility for either of the two terms to be positive is when
n = 0 and |m| > 1, or |n| > 1 and m = 0
Now for the case when m = 0 and |n| > 1
|m + n| < 5
|0 + n| < 5
So n can be ±±2, ±±3, ±±4
Which are 6 cases
Similarly for the case when n = 1 and |m| > 1
|m + n| < 5
|0 + m| < 5
So m can be ±±2, ±±3, ±±4
Again we have 6 cases.
Hence the answer is 12.
CAT 2021 Quant Question:
The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is
A. 90000
B. 160000
C. 120000
D. 100000
Answer:
Let the length be x and the breadth be y,
Then the area of the region will be
x×y = 60000
Then the cost of fencing the region will be
200x + 100x + 100y + 100y
300x + 200y
Now we know that the Arithmetic mean ≥ Geometric mean.
So,
300x + 200y ≥ 2 (60000)
300x + 200y ≥ 120000)
So we can say the cost will always be greater than 120000
The answer is 120000
Choice C is the correct answer.
CAT 2021 Quant Question:
If 
is a positive integer such that 
then the smallest value of is
Answer:
Hence, the answer is 6
CAT 2021 Quant Question:
Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is
A. 2436
B. 3436
C. 2346
D. 1436
Answer:
Bank A has a rate of interest of 6% and compounds half yearly.
This is the same as having a 3% interest rate per half-year.
So, if a Principal, P is invested for an year in bank A, at the end of the year it becomes P(1.03)(1.03) = P(1.0609)
Therefore the interest rate when viewed as a Simple interest scheme is 6.09% per annum.
Rupa invested in Bank C, which has twice the interest rate as Bank B and the quantum for which the investment is made is also double, hence Rupa effectively gets 4 times the interest that Raju gets for the same investment in Bank A.
Let’s say Raju invested ₹ 10,000 in Bank B.
Since this is the same as investing in Bank A for 1 year, his interest would be 6.09% of 10,000 = ₹ 609.
Now, for the same investment, Rupa must earn 4 times that of ₹ 609
So, Rupa earns ₹ 2,436
The answer is '2436’
Choice A is the correct answer.
Answer:
g(x) = x + 3
f(x) = 
- 7x
f(g(x)) - 3x
= f(x + 3) - 3x
= 
- 7(x + 3) - 3x
= + 9 + 6x - 7x - 21 - 3x
= - 4x - 12
= - 4x + 4 - 4 - 12
= - 4x + 4 - 16
= 
- 16
f(g(x)) - 3x is minimum when - 16 is minimum.
- 16 is minimum when is minimum.
Since is non-negative, the minimum value it can take is 0.
Hence the minimum value of - 16 = 0 - 16 = -16
Therefore, the minimum value of f(g(x)) - 3x is -16
Hence, the answer is '- 16’
Choice D is the correct answer.
The best way to improve your VARC skill is Reading. Read tons of stuff from Bharath’s Curated Reading list and get a wonderful VARC score.
The passage below is accompanied by a set of questions. Choose the best answer to each question.
The sleights of hand that conflate consumption with virtue are a central theme in A Thirst for Empire, a sweeping and richly detailed history of tea by the historian Erika Rappaport. How did tea evolve from an obscure “China drink” to a universal beverage imbued with civilising properties? The answer, in brief, revolves around this conflation, not only by profit-motivated marketers but by a wide variety of interest groups. While abundant historical records have allowed the study of how tea itself moved from east to west, Rappaport is focused on the movement of the idea of tea to suit particular purposes.
Beginning in the 1700s, the temperance movement advocated for tea as a pleasure that cheered but did not inebriate, and industrialists soon borrowed this moral argument in advancing their case for free trade in tea (and hence more open markets for their textiles). Factory owners joined in, compelled by the cause of a sober workforce, while Christian missionaries discovered that tea “would soothe any colonial encounter”. During the Second World War, tea service was presented as a social and patriotic activity that uplifted soldiers and calmed refugees.
But it was tea’s consumer-directed marketing by importers and retailers “ and later by brands “ that most closely portends current trade debates. An early version of the “farm to table” movement was sparked by anti-Chinese sentiment and concerns over trade deficits, as well as by the reality and threat of adulterated tea containing dirt and hedge clippings. Lipton was soon advertising “from the Garden to Tea Cup” supply chains originating in British India and supervised by “educated Englishmen”. While tea marketing always presented direct consumer benefits (health, energy, relaxation), tea drinkers were also assured that they were participating in a larger noble project that advanced the causes of family, nation and civilization. . . .
Rappaport’s treatment of her subject is refreshingly apolitical. Indeed, it is a virtue that readers will be unable to guess her political orientation: both the miracle of markets and capitalism’s dark underbelly are evident in tea’s complex story, as are the complicated effects of British colonialism. . . . Commodity histories are now themselves commodities: recent works investigate cotton, salt, cod, sugar, chocolate, paper and milk. And morality marketing is now a commodity as well, applied to food, “fair trade” apparel and eco-tourism. Yet tea is, Rappaport makes clear, a world apart “ an astonishing success story in which tea marketers not only succeeded in conveying a sense of moral elevation to the consumer but also arguably did advance the cause of civilisation and community.
I have been offered tea at a British garden party, a Bedouin campfire, a Turkish carpet shop and a Japanese chashitsu, to name a few settings. In each case the offering was more an idea “ friendship, community, respect “ than a drink, and in each case the idea then created a reality. It is not a stretch to say that tea marketers have advanced the particularly noble cause of human dialogue and friendship.
CAT 2021 VA RC Question:
Q. 1. The author of this book review is LEAST likely to support the view that:
A. tea drinking was sometimes promoted as a patriotic duty.
B. the ritual of drinking tea promotes congeniality and camaraderie.
C. tea drinking has become a social ritual worldwide.
D. tea became the leading drink in Britain in the nineteenth century.
Answer:
Except option D, all other options are mentioned in the passage.
‘I have been offered tea at a British garden party, a Bedouin campfire, a Turkish carpet shop and a Japanese chashitsu, to name a few settings. In each case the offering was more an idea “ friendship, community, respect “ than a drink, and in each case the idea then created a reality.’ From these lines, we know options B and C are true.
Option A is also true: ‘During the Second World War, tea service was presented as a social and patriotic activity that uplifted soldiers and calmed refugees’.
The author, however, does not say that tea became the leading drink in Britain in the nineteenth century. So, the author is least likely to support option D.
Hence, the answer is tea became the leading drink in Britain in the nineteenth century.
Choice D is the correct answer.
CAT 2021 VA RC Question:
Q. 2. This book review argues that, according to Rappaport, tea is unlike other “morality” products because it:
A. appealed to a universal group and not just to a niche section of people.
B. had an actual beneficial effect on social interaction and society in general.
C. was actively encouraged by interest groups in the government.
D. was marketed by a wide range of interest groups.
