Each question is followed by two statements labelled as I and II. Dec...
Question:
Given below is an equation where the letters represent digits. (PQ). (RQ) = XXX. Determine the sum of P Q R X.
Statements:
I. X = 9.
II. The digits are unique.
Answer:
Neither Statement I nor Statement II is necessary to answer the question.
Explanation:
To determine the sum of P, Q, R, and X, we need to determine the values of P, Q, R, and X individually. However, we cannot determine the values of these variables based on the given equation alone. Therefore, neither Statement I nor Statement II alone is sufficient to answer the question.
Statement I tells us the value of X is 9, but we still cannot determine the values of P, Q, and R. It is possible that P = 1, Q = 2, R = 3, and X = 9 or P = 3, Q = 3, R = 3, and X = 9. Therefore, Statement I alone is not sufficient to answer the question.
Statement II tells us that the digits are unique, but we still cannot determine the values of P, Q, R, and X. It is possible that P = 1, Q = 2, R = 3, and X = 9 or P = 9, Q = 8, R = 7, and X = 9. Therefore, Statement II alone is not sufficient to answer the question.
Hence, we need both statements together or additional information to determine the values of P, Q, R, and X. Therefore, the correct answer is option D.
Each question is followed by two statements labelled as I and II. Dec...
PQ. RQ = XXX
Therefore, X is the unit’s digit of Q2 and X can be 1 or 4 or 5 or 6 or 9, since the unit’s digit of square of any number will have only one of these digits.
If X = 111 = 37 X 3, which is invalid as it not of the form PQ. RQ.
If X = 444 = 37 X 12, which is invalid as it not of the form PQ. RQ.
If X = 555 = 37 X 15, which is invalid as it not of the form PQ. RQ.
If X = 666 = 37 X 18, which is invalid as it not of the form PQ. RQ.
If X = 999 = 37 X 27, which is valid as it not of the form PQ. RQ.
Therefore, P + Q + R + X = 3 + 7 + 2 + 9 = 21
Hence, none of the statements are necessary to answer the question.
Hence, the correct option is (d).