CAT 50 Day Streak – Day 3
30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA
VARC · Verbal Ability & Reading Comprehension
Well, supposedly. If you ask an economist, they will almost certainly tell you that a recession is indicated by things such as mounting unemployment, falling industrial production, and short-term interest rates rising relative to long-term ones. Suppose you ask the people working at the National Bureau of Economic Research, who actually make the call about a recession. In that case, they will say it is a “significant decline in economic activity that is spread across the economy and that lasts more than a few months.” They are highly unlikely to tell you that the best way to understand the state of global markets is to take a look at your ankles.
That’s not to say that pop-culture recession indicators are meaningless. A recession is a phenomenon necessarily defined in hindsight, usually long after life has changed on the ground: The Great Recession officially began at the end of 2007, but the NBER didn’t announce that it had until the following December, right around when more than half a million people lost their jobs in a single month. Consumer behaviour is a reactive measure of how much money people have in their pockets, which is probably why Greenspan was apparently paying attention to underwear. Many other pop-culture recession indicators—including the rise in law-school applications, the decline in demand for cardboard boxes, and the growing use of libraries and generic products—have been validated as useful signals about the health of the economy. They currently show what the more traditional indicators also show: The American economy is full of uncertainty, even though it has not yet tipped officially into recession.
But taking anecdotal intuition about individual consumer psychology and extrapolating widely can lead to some odd and unhelpful conclusions. The way people spend their money is personal, and the product of a complex set of factors. It’s also sometimes illogical. Case in point: In 2008, when the Nielsen Company analysed consumer behaviour during a recession, the firm’s findings indicated that whereas candy is recession-proof, soda—liquid candy—is among the most recession-prone consumer goods. And societies don’t respond to crises the same way every time. The hemline index, which holds that in bad times hemlines go down and in good times they rise, is one of the most cited pop-culture recession indicators. It originated in the 1920s, when most women didn’t work outside the home, styles were far more rigid, the fashion industry operated completely differently, and the miniskirt did not exist. Even if it were possible to reliably measure hemlines on a large scale, they are also influenced, in the short and long term, by trends, weather, and norms. Economic anxiety is a powerful force, but it is not the only force dictating the way people act.
Here is what we know, according to Joanne Hsu, who runs the University of Michigan’s consumer-sentiment survey program. Generally speaking, the less money people feel like they have, the more likely they are to skip big expenses and to substitute cheaper, lower-quality goods where they can. They seek out stress relief, good deals, and cheap indulgence.
The passage is balanced. Pop-culture indicators are “not meaningless” and some have been validated (the sense), but extrapolating from them “can lead to some odd and unhelpful conclusions” (the nonsense). D captures both sides.
A overstates (“the only indicators you need”). B turns a passing mention of Greenspan into the theme. C focuses on one example and on prediction in general, not on pop-culture indicators.
The NBER defines a recession as a “significant decline in economic activity that is spread across the economy and that lasts more than a few months”. B paraphrases exactly this.
A and C mix in pop-culture signals (generic products, law-school applications). D describes the pop-culture approach, not the official one.
The author defends pop-culture indicators by noting that a recession is “defined in hindsight”: the NBER announced the 2007 recession a year late. Consumer behaviour, by contrast, is a reactive, on-the-ground measure. Their value is immediacy.
B (“greater accuracy”) and D (“reliable, standalone”) overstate the case. C is not claimed: the passage says spending is complex and sometimes illogical.
A (trends, weather, norms), B (the hemline index dates from the 1920s) and D (“not the only force dictating the way people act”) are all complications the passage raises.
C is not a complication, and it is false: economists point to traditional indicators, not pop-culture ones.
“This” in “To resolve this” needs a problem as its antecedent. That problem is stated just before blank 2: distortions that look like fossils but are deformed rocks. After the techniques are mentioned, “At this point, we are as confident as we can be” follows naturally.
At blank 1 the problem hasn’t been stated yet. At blanks 3 and 4 the matter is already settled.
- As more individuals are produced than can survive, there must in every case be a struggle for existence.
- The earliest fossil forms known to us already indicate the perfection of many modern groups, which cannot be reconciled with gradual struggle.
- Hence it comes to pass that the balance of nature is kept even by a complicated web of relations.
- If some plants or animals vary ever so little in habits or structure, and are advantaged in relation to their conditions of life, they will tend to survive.
- The amount of food for each species, of course, gives the extreme limit to which each can increase; but very frequently it is not the obtaining food, but some other check, which determines the average number of a species.
Sentences 1, 4, 5 and 3 build a single Darwinian argument, in the order 1 → 4 → 5 → 3:
- 1: More individuals are produced than can survive, so there is a struggle for existence.
- 4: Those with slight advantageous variations tend to survive.
- 5: Numbers are limited by food and other checks.
- 3: “Hence” the balance of nature is kept by a web of relations.
Sentence 2 argues against gradual struggle, using the fossil record. It contradicts the paragraph’s line of thought rather than extending it.
D covers all three points: minorities are disproportionately affected by testing, there are no racial patterns in drug use, and wealth is the factor that stands out.
A contradicts the passage (no clear pattern by education). B contradicts it (no racial pattern). C invents both the “equally applied” claim and minorities “resisting” tests.
The sentence opens with “Or upholding…”, a gerund phrase that continues a list of “apparently illogical things”. The last sentence ends with just such an example, “like giving away your personal wealth for public good”. The new sentence adds a second example, so it belongs at blank 4.
At blanks 1–3, there is no preceding example for “Or” to continue.
- To illustrate: two people can view the same event yet reach entirely different conclusions about its connotation.
- The solution, then, is to somehow avoid setting off such impulses that are beyond the control of our conscious mind—something that is easier said than done.
- The idea is to view everything with an objective mindset and avoid the “jumping to conclusions” syndrome, which can trigger these unwanted impulses.
- One way of doing so is to gain a better understanding of how we perceive different events around us.
The order runs like this:
- 2: States the solution: avoid setting off such impulses, which is “easier said than done”.
- 4: “One way of doing so” is to understand how we perceive events.
- 3: “The idea is” to stay objective and avoid jumping to conclusions.
- 1: “To illustrate”: two people read the same event differently.
- Online stores are highly competitive not only with other online stores, but also with brick-and-mortar competitors.
- Point-of-sale advantages include stores offering no shipping charges and free ship-to-store options.
- The internet can be a great resource for shoppers looking to expand their choices of products to buy and an invaluable way of saving money.
- Price-comparison websites make deal hunting easier and also help guide shoppers to online stores with the best reputations by posting reviews submitted by other shoppers.
The order runs like this:
- 3: General opener: the internet helps shoppers widen choice and save money.
- 1: Online stores are highly competitive.
- 4: Price-comparison sites intensify that competition and guide shoppers.
- 2: The point-of-sale advantages stores offer to win customers.
DILR · Data Interpretation & Logical Reasoning
A library has five shelves – A, B, C, D and E. The table below gives the ratio of fiction and non-fiction books kept in those shelves, and also the ratio of books by Indian and foreign authors.
| Shelf | Fiction : Non-Fiction | Indian : Foreign authors |
|---|---|---|
| A | 3 : 2 | 4 : 1 |
| B | 5 : 3 | 3 : 1 |
| C | 9 : 5 | 5 : 2 |
| D | 7 : 6 | 2 : 1 |
| E | 4 : 3 | 5 : 3 |
Each shelf’s total must be a multiple of both ratio sums, i.e. of their LCM.
| Shelf | F:NF sum | I:F sum | Unit (LCM) | Fiction / unit | Non-fiction / unit | Indian / unit | Foreign / unit |
|---|---|---|---|---|---|---|---|
| A | 5 | 5 | 5 | 3 | 2 | 4 | 1 |
| B | 8 | 4 | 8 | 5 | 3 | 6 | 2 |
| C | 14 | 7 | 14 | 9 | 5 | 10 | 4 |
| D | 13 | 3 | 39 | 21 | 18 | 26 | 13 |
| E | 7 | 8 | 56 | 32 | 24 | 35 | 21 |
With one unit on every shelf (minimum 122 books), non-fiction = 2 + 3 + 5 + 18 + 24 = 52.
Total = 5a + 8b + 14c + 39d + 56e, with each coefficient ≥ 1. The minimum is 122, and any extra must be built from units of 5, 8, 14, 39 and 56.
- 135: extra 13 = 5 + 8 ✓
- 136: extra 14 = 14 ✓
- 137: extra 15 = 5 + 5 + 5 ✓
- 134: extra 12 can’t be made from 5, 8 and 14 ✗
So 134 is impossible.
The extra over 122 is 56. At the base, Indian = 4 + 6 + 10 + 26 + 35 = 81. The 56 extra books can be split in several ways:
- One more E unit (56): Indian = 81 + 35 = 116
- Four more C units (56): Indian = 81 + 40 = 121
- Seven more B units (56): Indian = 81 + 42 = 123
Other splits exist too. Since different splits give different answers, it cannot be determined.
B, C and E must each hold a common multiple of 8, 14 and 56, so at least 56 each. A = 5 and D = 39 at minimum.
Fiction: A 3 + B 35 + C 36 + D 21 + E 32 = 127.
With equal shelf sizes, compare the foreign fractions: A 1/5 = 0.20, B 1/4 = 0.25, C 2/7 ≈ 0.29, D 1/3 ≈ 0.33, E 3/8 = 0.375.
Shelf E has the most books by foreign authors (option D).
The extra over 122 is 18. The only way to make it is 5 + 5 + 8, i.e. two more A units and one more B unit. So A = 15, B = 16, C = 14, D = 39 and E = 56.
Fiction = 9 + 10 + 9 + 21 + 32 = 81, and non-fiction = 140 − 81 = 59.
Difference = 22.
An animal stable has five consecutive enclosures, numbered 1 through 5 from left to right, for housing exactly seven animals – four goats and three sheep.
- Five of the animals are female and two are male.
- No enclosure houses more than two animals.
- No enclosure houses both a goat and a sheep.
- No female goat is kept in an enclosure that is immediately next to an enclosure housing a male sheep.
Sheep can’t share with goats, and an enclosure holds at most 2. So 3 sheep split as 2 + 1 or 1 + 1 + 1. Either way, at least one sheep is alone.
The others need not hold. For example, 1: 2 goats, 2: 2 goats, 3: empty, 4: male sheep, 5: female + male sheep is valid. There, no female is alone (A fails). In another arrangement, both males can be goats sharing an enclosure, which makes C and D fail.
Only enclosures 1, 2, 4 and 5 are usable. 4 goats need 2 enclosures (2 each), and 3 sheep use the other 2 (2 + 1).
Goat enclosures can’t be adjacent, so each of the pairs {1, 2} and {4, 5} holds one goat enclosure and one sheep enclosure. That makes C (no goat alone) and D (the sheep enclosures are never adjacent) always true.
Every sheep enclosure is next to a goat enclosure. A male sheep would force both goats beside it to be male, making 3 males. So no sheep is male, and B is always true.
The goats could be in 1 and 4, for example, so A could be false.
The sheep take 3 enclosures and the 4 goats take 2 (2 each), so all 5 enclosures are used. Both males must be sheep, leaving 1 female sheep.
The two male-sheep enclosures can’t touch a goat enclosure. The only arrangements that work are G G F M M and M M F G G, with the female sheep always in the middle.
So Enclosure 3 can never hold a goat.
Both males are the sheep in enclosure 4, so all goats are female. Enclosures 3 and 5 are next to 4, so they can’t hold goats. All 4 goats must go in enclosures 1 and 2, two each.
The one remaining (female) sheep goes alone in enclosure 3 or 5.
A, B and C are impossible. D could be true.
QA · Quantitative Ability
From the conditions: 3r2 = 3 + 3d and 3r4 = 3 + 15d. So r2 = 1 + d and r4 = 1 + 5d.
Then (1 + d)2 = 1 + 5d, which gives d2 = 3d, so d = 3 (d ≠ 0 for a non-constant sequence).
7th term = 3 + 6 × 3 = 21.
Take CP of a notebook = 5 and CP of a pen = 3.
4 × 5 = 20 = SP of 5 pens, so SP of a pen = 4. And 8 × 3 = 24 = SP of 3 notebooks, so SP of a notebook = 8.
CP = 8 and SP = 12 for the pair, so profit = 4/8 = 50%.
Let Pushkin’s speed be w steps/s and the escalator’s speed e steps/s.
During the 9 s failure he loses 9e steps of help. He makes these up at the combined speed (w + e), so 9e/(w + e) = 7. This gives 2e = 7w, i.e. e = 3.5w.
While he walks 80 steps, the escalator moves 3.5 × 80 = 280 steps. Total = 80 + 280 = 360.
Both roots are real only if x − 1 ≥ 0 and 1 − x ≥ 0, so x = 1. The LHS is then 0.
(2 − y)2 = 0 gives y = 2. So x + 2y = 1 + 4 = 5.
s = 30, so the base area = √(30 × 24 × 5 × 1) = √3600 = 60.
The largest altitude falls on the shortest side: 2 × 60 ÷ 6 = 20, so the prism height is 20.
TSA = perimeter × height + 2 × base = 60 × 20 + 2 × 60 = 1200 + 120 = 1320.
The total is 325. Work backwards from the last entry.
- The first four must sum to a multiple of 4. 325 ≡ 1 (mod 4), so the 5th value ≡ 1 (mod 4), which is 77. The remaining four sum to 248.
- The first three must sum to a multiple of 3. 248 ≡ 2 (mod 3), so the 4th value ≡ 2 (mod 3), which is 59. The remaining three are 55, 64, 70 (sum 189 ✓).
- The first two must have an even sum, so they are 64 and 70. That leaves 55 as the 3rd value.
The base is ((x − 5)2 + 1)/5, which is always positive. So ab = 1 only when the base = 1 or the exponent = 0.
- Base = 1: x2 − 10x + 26 = 5, i.e. x2 − 10x + 21 = 0, so x = 3, 7.
- Exponent = 0: x2 − 6x + 5 = 0, so x = 1, 5 (the base is non-zero at both).
- A base of −1 is impossible because the base is always positive.
The roots are 1, 3, 5 and 7, so the sum is 16.
By the triangle inequality, 2 < x < 10 and 2 < y < 10.
So |x − y| can take any value in [0, 8) but never reaches 8. The smallest positive integer that isn’t possible is 8.
Let the volume be V. Milk goes from (3/4)V to (1/3)V after two replacements:
(3/4)(1 − 32/V)2 = 1/3, so (1 − 32/V)2 = 4/9 and 1 − 32/V = 2/3.
V = 96 litres.
There are 9 cubes and 8 are used, so exactly one cube is left out.
- Leave out a black: 8!/(1! 3! 4!) = 280
- Leave out a red: 8!/(2! 2! 4!) = 420
- Leave out a yellow: 8!/(2! 3! 3!) = 560
Total = 280 + 420 + 560 = 1260.
Correct: 0 · Wrong: 0 · Accuracy: 0%
Keep the streak alive. See you tomorrow for Day 4.
