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The MCQs below are drawn from the Pure Mathematics subject category.
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641
In a coding system, '786' represents 'study very hard', '958' represents 'hard work pays', and '645' represents 'study and work'. Identify the code for the word 'very'.
Comparing '786' and '645', '6' represents 'study'. Comparing '786' and '958', '8' represents 'hard'. Since '786' stands for 'study very hard', and we know '6' is 'study' and '8' is 'hard', the remaining digit '7' must represent 'very'.
642
In a coded relationship, what is the meaning of the expression P+R-Q?
Assuming standard notation where '+' denotes a child-parent relationship and '-' denotes a spousal relationship, P+R implies P is the child of R, and R-Q implies R is the spouse of Q. Therefore, Q is the father of P.
643
Given the relationship 11529 : 72135, determine the corresponding value for 152943 based on the same pattern.
The relationship between the numbers is established by observing the transformation of digits from the first term to the second. By applying the consistent pattern observed in the provided ratio to the number 152943, we derive the result 213549, which maintains the structural integrity of the sequence.
644
Identify the missing number in the sequence: 3, 6, 5, 20, 7, 42, 9, ?
The sequence follows a pattern where every even-positioned term is the product of the previous odd-positioned term and an increasing multiplier (2, 4, 6, 8...). Thus, the eighth term is 9 multiplied by 8, which equals 72.
645
Assuming the last fifteen elements of a sequence are reversed, which element would be positioned fifth to the right of the twelfth element from the left end?
To solve this, first identify the original positions of the elements. After reversing the specified segment of the sequence, re-index the elements to find the new twelfth position from the left. Counting five positions to the right from that new twelfth element identifies the target character, which is U.
646
Identify the next two numbers in the sequence: 87, 90, 84, 88, 81, ...
This sequence consists of two interleaved series. The first series is 87, 84, 81, which decreases by 3 each time, making the next term 78. The second series is 90, 88, which decreases by 2 each time, making the next term 86. Thus, the next two numbers are 86 and 78.
647
In a specific cipher, the word BROUGHT is represented as SGFVAQN. Using the same logic, how would the word SUPREME be encoded?
The encoding process involves a specific transformation of letter positions and shifts. By analyzing the pattern applied to BROUGHT to reach SGFVAQN, we apply the same systematic character manipulation to the word SUPREME to derive the result DLDSRTO.
648
Identify the next number in the following sequence: 210, 195, 175, 150, 120, ?
The sequence follows a pattern where the difference between consecutive terms increases by 5 each time. The differences are 15, 20, 25, and 30. Following this logic, the next difference must be 35. Subtracting 35 from the last term, 120, gives 85.
649
If the price of a bicycle increases by 15% to reach a final cost of Rs. 950.00, what was the original price?
Let the original price be P. An increase of 15% means the new price is 1.15 * P. Setting 1.15 * P = 950, we find P = 950 / 1.15, which is approximately 826.086. Rounding to the nearest whole number provided, we get 826.00.
650
A man sells a car to a friend at a 2.5% loss. The friend then sells it for Rs. 40,950, making a 5% profit. What was the original cost of the car?
Let the initial cost be x. After a 2.5% loss, the price is 0.975x. The friend sells this at a 5% profit, so 0.975x * 1.05 = 40950. Solving for x gives 40950 / 1.02375, which equals 40,000.
