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7 cannibals of XYZ island, decide to throw a party. As you may be aware, cannibals are guys who eat human beings. The senior among them – Father Cannibal decides that any 6 of them will eat up one cannibal, then out of the remaining six – five of them will eat up one cannibal and so on till one is left. What is the time until one cannibal is left, if it takes one cannibal 3 hours to eat up one cannibal independently?
1. 7 hrs 11 min
2. 6 hrs 12 min
3. 7 hrs 21 min
4. 18 hrs 16 min
Answer: Option C
At the beginning 6 cannibals will eat one, so time required will be 180/6 = 30 min.
Then out of the remaining six – five will devour one, so time required will be 180/5 = 36 min.
Thus the time until one cannibal is left will be = (180/6 + 180/5 + 180/4 + 180/3 + 180/2 + 180/1) min
= (30 + 36 + 45 + 60 + 90 + 180) min
= 441 min
= 7 hrs 21 min.
Hence option 3.

Three articles are purchased for Rs. 1050, each with a different cost. The first article was sold at a loss of 20%, the second at 1/3rd gain and the third at 60% gain. Later he found that their SPs were same. What was his net gain/loss?
1. 14.28% gain
2. 13% loss
3. 12% loss
4. 11.11% gain
Answer: Option A
Let us assume that their CPs are x, y & z respectively.
According to the given condition 0.8x = 1.33y = 1.6z
⇒ (80/100)x = 400y/(3 × 100) = (160/100)z
⇒ x : y = 5 : 3 & y : z = 6 : 5
Thus x : y : z = 10 : 6 : 5
Hence CPs of the articles are x = (10/21) × 1050 = 500,
y = (6/21) × 1050 = 300 &
z = (5/21) × 1050 = 250.
SP of the article with CP Rs. x is 0.8x = 0.8 × 500 = 400.
Since SPs are same, the total SP will be 400 × 3 = 1200.
Hence the gain % = (SP – CP)/CP × 100 = (1200 – 1050)/1050 × 100 = 14.28%.
In the figure below, line DE is parallel to line AB. If CD = 3 and AD = 6, which of the following must be true?
1. ΔCDE ≈ ΔCAB
2. (area ΔCDE / area ΔCAB) = (CD/CA)²
3. If AB = 4, then DE = 2
1. I and II only
2. I and III only
3. II and III only
4. I, II and III
Answer: Option A
Since the lines are parallel, Triangle CDE is similar to TriangleCAB and hence statements I and II are true.
However, the ratio CD : CA = 3:9
So,If AB = 4, then DE = 4/3. So statement III is false Hence option A
In a game of tennis, A gives B 21 points and gives C 25 points. B gives C 10 points. How many points make the game?
1. 50
2. 45
3. 35
4. 30
Answer: Option C
When B scored p -10 then C scored p - 25.
When B scores 1 then C scores (p-25)/(p-10)
So when B scores p points then C will score (p-25)/(p-10) × p
As per question (p-25)/(p-10) × p = p -10 . Solving this we get p = 35

A B C

p points (p-21) points (p-25) points

p points (p-10) points
What is the value of a if x³ + 3x² + ax + b leaves the same remainder when divided by (x – 2) and (x + 1)?
1. 18
2. 3
3. -6
4. Cannot be determined
Answer: Option C
Suppose the remainder is R.
Substituting x = 2 and x = –1, we get R = 8 + 12 + 2a + b = –1 + 3 – a + b
⇒ 3a = –18
⇒ a = –6

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What is the range of values of k if (1 + 2k)x² – 10x + k – 2 = 0 has real roots?
1. –3 ≤ k ≤ 4.5
2. –1.5 ≤ k ≤ 9
3. k ≥ 4.5, k ≤ –3
4. k ≥ 3, k ≤ –9
Answer: Option A
Since the given expression has real roots, we know that (–10)² – 4(1 + 2k)(k – 2) ≥ 0
100 – 8k² + 12k + 8 ≥ 0
8k² – 12k – 108 ≤ 0
2k² – 3k – 27 ≤ 0
–3 ≤ k ≤ 9/2
A square, S₁, circumscribes the circum circle of an equilateral triangle of side 10 cm. A square, S₂, is inscribed in the in circle of the triangle. What is the ratio of the area of S₁ to the area of S₂?
1. 4:1
2. 32:1
3. 8:1
4. 2:1
Answer: Option C
The height of the equilateral triangle is 5√3 cm.
Since the height is also the median, we know that the circum-radius is 2/3 × 5√3 = 10√3/3 and the in-radius is 1/3 × 5√3 = 5√3/3.
The diameter of the circumcircle is the side of square S₁.
So the area of S₁ is (2 × 10√3/3)²= 1200/9.
The diameter of the in-circle is the diagonal of square S₂.
So the area of S₂ is ½ × (2 × 5√3/3)² = 300/18.

Thus the ratio of areas S₁ : S₂is 1200/9 : 300/18 = 8 : 1
The sum of the first n terms of an AP is S_n = 4n² – 2n. Three terms of this series, T₂, T_m and T₃₂ are consecutive terms in GP. Find m
1. 7
2. 10
3. 16
4. 5
Answer: Option A
Explanation: From the given information, S₁= 4 × 12 – 2 × 1 = 2 => T₁ = 2. Now, S₂ = 4 × 22 – 2 × 2 = 12.
Since S₂ = T₁ + T₂ and T₁ = 2, we get T₂ = 10. So, the 1st term of the AP is 2 and the common difference is 8.
From this, we get T₃₂ = 2 + 31 × 8 = 250.
Since T₂, T₃ and T₃₂ are consecutive terms in GP, we know that T_m / T₂ = T₃₂ / T_m
⇒ (T_m)²= T₂ × T₃₂ = 2500
⇒ T_m = 50.

Three casks of equal capacities contain three liquids A, B & C in the ratio 1 : 2 : 3, 3 : 4 : 5 & 5 : 6 : 7 respectively. The mixtures from these casks are taken in the ratio 1 : 2 : 3 and poured into a 4th cask with the same capacity as that of the three casks and the cask is completely filled. What is the ratio of the liquids A, B and C in the resulting mixture?

25:36:47
16:21:26
3:4:5
1:2:3

Answer: Option C
(1 + 2 + 3) = 6, (3 + 4 + 5) = 12 & (5 + 6 + 7) = 18
Common multiple of (6, 12 , 18) = 36
So let us fix the capacities of four casks as 36 liters each.

	Liquid A	Liquid B	Liquid C
Cask 1(36 liters)	6	12	18
Cask 2(36 liters)	9	12	15
Cask 3(36 liters)	10	12	14

Since the mixtures are taken in the ratio 1 : 2 :3, 6 liters, 12 liters and 18 liters mixture are drawn from the three casks respectively.

	Liquid A	Liquid B	Liquid C
Cask 1(6 liters)	1	2	3
Cask 2(12 liters)	3	4	5
Cask 3(18 liters)	5	6	7
Cask 4(36 liters)	9	12	15

Hence the ratio of the liquids in the resulting mixture is 9 : 12 : 15 = 3 : 4 : 5
Hence option C

A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total. If he sold one of the bullocks at a gain of 20%, the other is sold at a loss of
1. 20 %
2. 18%
3. 14%
4. 21 %
5. None of these
Answer: Option A
A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total.
As he sold one bullocks at a gain of 20%, it means 120% of C.P = 8400
We get C.P of one bullock = 7000
So gain on one bullock = Rs 1400
Other bullocks is sold at lose and there is neither losing nor gaining in total
So loss on 2nd bullock = 1400/7000×100 = 20%