Motorola – Aptitude Questions & Answers for Placement Tests
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Q.1 When m is divided by 7, the remainder is 3. When 4m is divided by 7, the remainder is
Check Solution
Ans: A
If m leaves a remainder of 3 when divided by 7, we can represent m as 7k + 3, where k is an integer. Then, 4m = 4(7k + 3) = 28k + 12. Dividing 4m by 7, we get (28k + 12)/7 = 4k + 1 + 5/7. Therefore, the remainder is 5.
Q.2 The value of 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 is
Check Solution
Ans: C
1/12 = 1/(3*4) = 1/3 – 1/4, 1/20 = 1/(4*5) = 1/4 – 1/5, 1/30 = 1/(5*6) = 1/5 – 1/6, 1/42 = 1/(6*7) = 1/6 – 1/7, 1/56 = 1/(7*8) = 1/7 – 1/8, 1/72 = 1/(8*9) = 1/8 – 1/9, 1/90 = 1/(9*10) = 1/9 – 1/10, 1/110 = 1/(10*11) = 1/10 – 1/11. Summing the series, we get 1/3 – 1/11 = 8/33.
Q.3 Let b = √(7 + 4√3) + √(7 – 4√3). Then we have
Check Solution
Ans: C
√(7 + 4√3) = √(4 + 3 + 4√3) = √(2^2 + (√3)^2 + 2 * 2 * √3) = √(2 + √3)^2 = 2 + √3. √(7 – 4√3) = √(4 + 3 – 4√3) = √(2^2 + (√3)^2 – 2 * 2 * √3) = √(2 – √3)^2 = 2 – √3. Therefore, b = 2 + √3 + 2 – √3 = 4.
Q.4 The largest among the numbers 1/4, 0.2, 2/5 and 0.35 is
Check Solution
Ans: C
Convert all numbers to decimals: 1/4 = 0.25, 2/5 = 0.4. Comparing 0.25, 0.2, 0.4, and 0.35, 0.4 is the largest.
Q.5 The smallest of the following numbers is 1/3, 0.34, 0.3, (0.3)2
Check Solution
Ans: D
Calculate each value: 1/3 ≈ 0.333, (0.3)2 = 0.09. Comparing, 0.09 is the smallest.
Q.6 If a tap can fill a tank in 6 hours, then the portion of the tank filled in 2 hours will be:
Check Solution
Ans: B
In 1 hour, the tap fills 1/6 of the tank. Therefore, in 2 hours, it will fill (1/6) * 2 = 1/3 of the tank.
Q.7 A shopkeeper marks the price of an item 40% above the cost price. He then offers a discount of 10% on the marked price. What is his profit or loss percentage?
Check Solution
Ans: A
Let the cost price be 100. Marked price = 100 + 40% of 100 = 140. Selling price = 140 – 10% of 140 = 140 – 14 = 126. Profit = 126 – 100 = 26. Profit % = (26/100) * 100 = 26%.
Q.8 An increase of 25% in the price of sugar enables a customer to purchase 5 kg less for Rs. 1000. The original price of sugar per kg is
Check Solution
Ans: A
Let the original price be P. Increased price = 1.25P. Difference in quantity bought = 5 kg. Original quantity = 1000/P. New quantity = 1000/(1.25P). 1000/P – 1000/(1.25P) = 5. 1000/P – 800/P = 5. 200/P = 5. P = 40.
Q.9 Two containers A and B contain mixtures of milk and water. In container A, the ratio of milk to water is 4:3, and in container B, the ratio is 5:2. If 28 liters of mixture from container A and 35 liters of mixture from container B are mixed together, what will be the ratio of milk to water in the resulting mixture?
Check Solution
Ans: A
In A, milk = (4/7)*28 = 16 liters, water = (3/7)*28 = 12 liters. In B, milk = (5/7)*35 = 25 liters, water = (2/7)*35 = 10 liters. Total milk = 16 + 25 = 41 liters. Total water = 12 + 10 = 22 liters. Ratio of milk to water in the new mixture = 41:22. There’s an error in the options. The closest approximation among options is:
Q.10 If X : Y = 2 : 3 and Y : Z = 9 : 4, then X : Z is
Check Solution
Ans: C
To find X:Z, we can manipulate the given ratios. From X:Y = 2:3, we have Y = (3/2)X. From Y:Z = 9:4, we have Y = (9/4)Z. Now we have (3/2)X = (9/4)Z. Rearranging, X/Z = (9/4)/(3/2) = (9/4)*(2/3) = 3/2.
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