SSC CGL Mock – Tier II Paper I Mock Test 03 – Section I · Part A · Mathematical Abilities | Online Quiz

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SSC CGL Mock – Tier II Paper I Mock Test 03 – Section I · Part A · Mathematical Abilities – 30 questions, subject: Full Mock Tests. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

The price of petrol rises by 20% and then by another 10%. A motorist cuts his consumption by 25%. What happens to his spending on petrol?

Correct Answer: B [It falls by 1%]

Explanation:

1.2 × 1.1 × 0.75 = 0.99 → spending falls by 1%.

A hemispherical vessel of inner radius 6 cm is full of syrup, which is to be filled into small cylindrical cups of base diameter 2 cm and height 3 cm. How many cups can be filled?

Correct Answer: C [48]

Explanation:

Vessel = 2/3 π × 216 = 144π; cup = π × 1 × 3 = 3π → 48 cups.

A rectangular plot is redrawn with its length 20% greater and its breadth 20% smaller. Compared with the original, the area of the plot:

Correct Answer: A [It decreases by 4%]

Explanation:

1.2 × 0.8 = 0.96 → the area falls by 4%.

The two parallel sides of a trapezium measure 20 cm and 10 cm, while the slanting sides measure 6 cm and 8 cm. What is the area of the trapezium?

Correct Answer: D [72 cm²]

Explanation:

Cut off a triangle with sides 6, 8 and 20 − 10 = 10: it is right-angled, so its height is 6 × 8/10 = 4.8 → area = 15 × 4.8 = 72 cm².

The average age of a committee of 8 members rises by 2 years when two men aged 35 and 45 are replaced by two women. What is the average age of the two women?

Correct Answer: A [48 years]

Explanation:

The women together are 80 + 8 × 2 = 96 years → average 48.

Find the smallest natural number that leaves remainders 1, 2, 3, 4 and 5 when divided by 2, 3, 4, 5 and 6 respectively.

Correct Answer: D [59]

Explanation:

Each remainder is one less than the divisor → number = LCM(2, 3, 4, 5, 6) − 1 = 60 − 1 = 59.

The seven-digit number 6413x2y (x, y digits) is divisible by 88. What is x + y?

Correct Answer: B [13]

Explanation:

88 = 8 × 11. Divisible by 11 → (6 + 1 + x + y) − (4 + 3 + 2) = x + y − 2 is 0 or 11 → x + y = 2 or 13; divisible by 8 → the last three digits x2y must be a multiple of 8.

Find the value of 1/(1 × 2) + 1/(2 × 3) + 1/(3 × 4) + … + 1/(19 × 20).

Correct Answer: A [19/20]

Explanation:

Each term = 1/k − 1/(k + 1); the sum telescopes to 1 − 1/20 = 19/20.

A alone needs 20 days for a job and B alone 30 days. They begin together, and A quits 5 days before the work is over. How many days does the whole job take?

Correct Answer: C [15 days]

Explanation:

A works (x − 5) days, B works x days: (x − 5)/20 + x/30 = 1 → 5x = 75 → x = 15.

10.

Ravi sold a watch at a profit of 12%. Had he bought it for 10% less and sold it for ₹ 192 less, he would have gained 20%. What was the cost price of the watch?

Correct Answer: A [₹ 4,800]

Explanation:

1.12C − 192 = 1.2 × 0.9C = 1.08C → 0.04C = 192 → C = 4,800.

11.

A dishonest grocer claims to sell at cost price, but his 1 kg weight actually weighs only 800 g, and what he weighs out contains 10% impurities. What is his true gain per cent?

Correct Answer: D [38 8/9%]

Explanation:

For the price of 1 kg of pure goods he gives 0.8 × 0.9 = 0.72 kg → gain = 0.28/0.72 = 38 8/9%.

12.

The simple interest on a sum is one-fourth of the sum, and the number of years equals the rate per cent per annum. What is the rate?

Correct Answer: B [5%]

Explanation:

P × r × r/100 = P/4 → r² = 25 → r = 5%.

13.

The mean of 10 observations is 20. Each observation is multiplied by 3 and then 5 is subtracted. What is the new mean?

Correct Answer: C [55]

Explanation:

Mean follows the same change: 3 × 20 − 5 = 55.

14.

A data set has standard deviation 4. Each value is multiplied by −3 and then 5 is added. What is the new standard deviation?

Correct Answer: A [12]

Explanation:

Adding a constant does not change spread; multiplying by −3 multiplies the SD by |−3| = 3 → 12.

15.

Meena draws a single card at random from a full pack of 52 playing cards. What is the probability that the card is either a face card or a spade?

Correct Answer: B [11/26]

Explanation:

12 face cards + 13 spades − 3 face cards that are spades = 22 → 22/52 = 11/26.

16.

A starts a business with ₹ 50,000. Some months later B joins with ₹ 75,000. At the end of the year the profit is shared in the ratio 8 : 9 (A : B). After how many months did B join?

Correct Answer: C [3 months]

Explanation:

50,000 × 12 : 75,000 × t = 8 : 9 → t = 9 months in business → joined after 3 months.

17.

A boat goes 30 km upstream and 44 km downstream in 10 hours, and 40 km upstream and 55 km downstream in 13 hours. What is the speed of the current?

Correct Answer: D [3 km/h]

Explanation:

Upstream speed 5 km/h, downstream 11 km/h → current = (11 − 5)/2 = 3 km/h.

18.

If x = 5 − √24, what is x² + 1/x²?

Correct Answer: B [98]

Explanation:

1/x = 5 + √24 → x + 1/x = 10 → x² + 1/x² = 100 − 2 = 98.

19.

If (x − 3) is a factor of x³ − 2x² + kx + 6, what is k?

Correct Answer: C [−5]

Explanation:

Put x = 3: 27 − 18 + 3k + 6 = 0 → k = −5.

20.

If a + b = 10, ab = 21 and a > b, find a³ − b³.

Correct Answer: A [316]

Explanation:

a − b = √(100 − 84) = 4; a² + b² = 100 − 42 = 58 → a³ − b³ = 4 × (58 + 21) = 316.

21.

Directions (Q 21–23): The pie chart shows how a family uses its monthly income of ₹ 80,000 (fictional data).

Pie chartThe family's savings are what per cent of its combined spending on Food and Rent?

Correct Answer: D [40%]

Explanation:

Answer: 40%. 18/45 × 100 = 40%.

22.

(Use the directions above – Q 21–23)
Pie chartWhat is the central angle of the combined sector for Education and Transport?

Correct Answer: A [90°]

Explanation:

Answer: 90°. (15 + 10)% of 360° = 90°.

23.

(Use the directions above – Q 21–23)
Pie chartNext month the rent rises by 10% while the income stays the same, and the extra rent is taken out of savings. What percentage of the income will the savings then be?

Correct Answer: C [16%]

Explanation:

Extra rent = 10% of 20% = 2% of income → savings = 18% − 2% = 16%.

24.

Diagram-basedABCD is a cyclic quadrilateral in which AB is a diameter of the circle and ∠ADC = 130° (see figure). Find ∠BAC.

Correct Answer: D [40°]

Explanation:

∠ABC = 180° − 130° = 50° (opposite angles); ∠ACB = 90° (semicircle) → ∠BAC = 40°.

25.

Circles of radius 6 cm and 3 cm are drawn with their centres 15 cm apart. A common tangent passes between the circles, crossing the line of centres. How long is this tangent between its points of contact?

Correct Answer: B [12 cm]

Explanation:

√(d² − (r₁ + r₂)²) = √(225 − 81) = 12 cm.

26.

A triangle has sides 10 cm, 17 cm and 21 cm. What is the height of the triangle measured to its longest side?

Correct Answer: B [8 cm]

Explanation:

s = 24; area = √(24 × 14 × 7 × 3) = 84 cm² → height = 2 × 84/21 = 8 cm.

27.

If 2 sin²θ + 3 cos θ = 3 and 0° < θ < 90°, find θ.

Correct Answer: D [60°]

Explanation:

2 − 2cos²θ + 3cos θ = 3 → 2cos²θ − 3cos θ + 1 = 0 → cos θ = ½ (cos θ = 1 gives θ = 0°) → θ = 60°.

28.

Given that the product sin θ · cos θ equals 1/4, evaluate sin⁶θ + cos⁶θ.

Correct Answer: C [13/16]

Explanation:

sin⁶ + cos⁶ = 1 − 3 sin²θ cos²θ = 1 − 3/16 = 13/16.

29.

Two vertical poles stand on level ground. From the foot of the shorter pole the top of the taller one is seen at 60°, and from the top of the shorter pole at 30°. If the shorter pole is 20 m high, how high is the taller one?

Correct Answer: A [30 m]

Explanation:

Let the gap be d: H = d√3 and H − 20 = d/√3 → H − H/3 = 20 → H = 30 m.

30.

Two jars contain milk and water in the ratios 4 : 1 and 2 : 3. Equal quantities from the two jars are poured into a third jar. What is the ratio of water to milk in the third jar?

Correct Answer: D [2 : 3]

Explanation:

Milk = 4/5 + 2/5 = 6/5, water = 1/5 + 3/5 = 4/5 → water : milk = 2 : 3.

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