Question : Directions: There are two numbers. The difference between these two numbers is 2 and the difference between their squares is 8. What are those numbers?
Option 1: 12, 10
Option 2: 3, 1
Option 3: 7, 5
Option 4: 8, 6
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Correct Answer: 3, 1
Solution : Given: Let the two numbers be a and b.
The difference between these two numbers is 2. ⇒ a – b = 2 ———— (1) And the difference between their squares is 8. ⇒ a2 – b2 = 8 As we know that a2 – b2 = (a – b)(a + b) Now, put the value of (a2 – b2) and (a – b) in a2 – b2 = (a – b)(a + b). ⇒ a2 – b2 = 2(a + b) ⇒ 8 = 2(a + b) ⇒ 4 = a + b ———— (2) Now, add the equations (1) and (2) – ⇒ a – b + a + b = 2 + 4 ⇒ 2a = 6 ⇒ a = 3 Now, put the value of a in equation (1) – ⇒ a – b = 2 ⇒ 3 – b = 2 ⇒ b = 1
So, the value of a is 3 and b is 1. Hence, the second option is correct.
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Question : Directions: Which of the following equations will be correct when the signs × and ÷ and the numbers 12 and 9 are interchanged?
Option 1: 12 + 8 × 9 + (24 ÷ 5 + 8) – 7 = 35
Option 2: 9 × 17 + 5 (24 ÷ 9) – 12 = 46
Option 3: 14 ÷ 2 + 10 (12 – 6) × 9 = 37
Option 4: 10 + 2 ÷ 3 + (24 × 9 + 8) – 12 = 17
Question : Directions: Which two numbers from amongst the given options should be interchanged to make the given equation correct? (42 ÷ 7) × 5 = 30 × 120 ÷ (10 + 5 × 2)
Option 1: 10 and 5
Option 2: 2 and 5
Option 3: 7 and 2
Option 4: 10 and 30
Question : Directions: From the given options, choose the correct one that will replace the question mark (?) in the following series. 2, 0, 3, 2, 4, 6, 5, 12, 6, ?, 7, 30
Option 1: 6
Option 2: 20
Option 3: 7
Option 4: 16
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (12, 9, 4) (18, 9, 6)
Option 1: (20, 12, 10)
Option 2: (14, 10, 7)
Option 3: (15, 12, 7)
Option 4: (12, 16, 3)
Question : Directions: From the given alternatives, select the one in which the set of numbers is most like the given set of numbers in the question. (14, 20, 3)
Option 1: (7, 13, 3)
Option 2: (5, 10, 15)
Option 3: (3, 6, 9)
Option 4: (4, 8, 16)
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