Test Q&As : Are you a Brainiac?

In this section, we shall explore several different types of questions from the various areas of entrance exams like the CAT, CET, GMAT, etc, and how to best solve them.

Quant

DIRECTIONS for questions 1: Choose the correct alternative.
1.   At a construction site, if the workers are 6 less than the usual number, the hours required to complete a task are 2 more than the usual but 7 less than what would be required if one-third of the workers were absent. How many hours will be required if there are 20 more workers than the usual?

1] 4 ½                         2] 12                         3] 13½                         4] Cannot be determined
Let 'x' workers take 'h' hours.

So, if one-third are absent, the rest will take 3h/2 hours
So, x – 6 workers take h + 2 hours which is equal to 3h/2 – 7.
So, h/2 = 9. So, h = 18
So, x – 6 workers take 20 hours instead of 18.
So, x / (x – 6) = 20 / 18  x = 60.
So, if 20 more workers are appointed, they will take 18 x 60 / 80 = 27/2 = 13½  hours.
Hence, [3].


2.   Find log 2 + log 3 + log 4 + log 5 … (n terms)
1]  1.5 log (n!)          2] n log {(n+1]!}³          3] log {(3n/2]!}          4] log {(n+1]!}3
log 2 + log 3 + log 4 + log 5 … (n terms)
= log {2^3/2 x 3^3/2 x 4^3/2 x 5^3/2 x ...... ⁽ⁿ⁺¹⁾}
= log { (n+1)! ^3/2 } =  log {(n + 1)!}³. Hence, [4].

3.     
Two circles are drawn inside a third circle, such that they touch each other externally and the large circle internally, such that the points of contact with the outer circle are diametrically opposite. The area of the larger circle is thus divided into 4 parts with areas p, q, r and s as shown in the figure. Then which of the following is true?
1] p + q = r + s                    2] pr = qs                    3] p + r = q + s                    4] p/q = r/s
Let the radii of the two smaller circles be a and b. Hence the radius of the larger circle will be
a + b. p = πa², r = πb² and the total area of the larger circle will be π(a + b)2.
The remaining area q + s = π(a + b)² – πa² – πb² = 2πab. Now, from the symmetry of the figure, q = s = πab. We can see that pr = qs = π²a²b².
Hence, [2].

Verbal

DIRECTIONS: This question has four sentences pertaining to a subject, which may or may not be in sequence. One of the sentences is contextually/logically incorrect. Choose the option corresponding to the sentence that is incorrect or inappropriate.

1. The Zhou centuries were a seminal time for China’s civilization, yet they get short shrift in some history books.
2. The third and the last of the pre-imperial ‘Three Dynasties’ (Xia, Shang, Zhou), the Zhou, supplanted the Shang as the supreme power in the lower Yellow River basin in c. 1045 BC, and would still be there nearly 800 years later.
3. None of China’s subsequent ruling lineages would last more than half as long; in fact the Zhou probably hold the world record for dynastic longevity.
4. In the course of this dynastic marathon, some thirty-nine kings followed one another, mostly in orderly father-to-son succession.

Explanation: Sentences [2], [3] and [4] – which can be arranged in the order [2]-[4]-[3] – all speak about the longevity of the Zhou dynasty, while [1] speaks of the importance of the time period, and its neglect in history books. Therefore, [1] does not fit into the context. Hence, [1].

DIRECTIONS: This question has a paragraph from which the last sentence has been deleted. From the given options, choose the option that completes the paragraph in the most appropriate way.
The idea that our mental terrain decides what information survives in our heads and what gets killed off finds a parallel with a venerable biological theory: Darwin’s theory of natural selection. When we see lions and polar bears, we marvel at how well these animals have adapted themselves to the savannah and the polar ice caps. But no committee of lions sat down and decided that the African savannah would be home. No electoral bear-college voted for a leader who called for polar bears to move to the Arctic.

1. These animals adapt to their environment by instinct, unlike humans, who do so with intelligence.
2. The savannahs and polar regions of our mind exist unknown to us, directing the way we adapt.
3. Our mental terrain has a topography that is as varied as the geography of the Earth, constantly directing us to adapt.
4. These animals did not adapt to their environment; their environment adapted them to it.  

Explanation: The paragraph is about the idea that it is the terrain of our mind that decides what survives inside our head and not we. To support this the author cites the examples of bears and lions and their respective habitats. The author says that the animals did not consciously decide or deliberate over their habitats. Since the main idea is about how our mental terrain or our mental environment decides what information survives, the concluding statement has to be about the animals’ environment and not they themselves deciding or choosing their habitat. Only option (4) does this. Option (1) is incorrect as the author is saying that we might in reality be using our intelligence. Options (2) and (3) make generalizations about human beings adapting and do not capture the specificity of the paragraph, which is the information surviving in our minds. Hence, [4].