Question

Fill in the blank :
Q4RT, ______ , QRT6, QR7T, Q8RT

• A. QTR7
• B. QR5T
• C. RQ9T
• D. TRQ6

Answer 1

The Correct Option is B

The correct option is (B): QR5T.

Answer 2

Ignoring the digits, every term is built from the same three letters in the same order, Q, then R, then T, with one digit inserted somewhere among them. Reading the digits across the series, 4, (missing), 6, 7, 8, they simply count upward by 1 each time, so the missing digit must be 5. Reading where that digit sits, term 1 'Q4RT' has it right after Q (position 2), term 3 'QRT6' has it at the very end (position 4), term 4 'QR7T' has it just before the final T (position 3), and term 5 'Q8RT' has it back after Q (position 2), the position swings 2, 3, 4, 3, 2, like a pendulum. So the missing second term needs the digit 5 sitting at position 3, giving Q, R, 5, T. Let's check the options against this:

1. Option A (QTR7): uses the digit 7, which belongs to the fourth term, not the second, and also rearranges the letters to Q, T, R instead of the fixed Q, R, T order.
2. Option B (QR5T): keeps the letters in the required Q, R, T order and places the digit 5, which comes right after 4 and before 6, at position 3, matching the pendulum pattern exactly.
3. Option C (RQ9T): starts with R instead of Q, breaking the fixed letter order, and uses the digit 9, one step beyond the last term's digit 8.
4. Option D (TRQ6): scrambles the letters into T, R, Q order and reuses the digit 6, which already belongs to the third term.

Only option B preserves the Q-R-T letter order and continues the digit sequence and position pattern correctly.

Therefore, the correct answer is QR5T.

Answer 3

Numbering the five terms 1 through 5 (Q4RT, ?, QRT6, QR7T, Q8RT), two independent formulas describe the pattern. First, the inserted digit equals the term number plus 3: term 1 gives \(1+3=4\), term 3 gives \(3+3=6\), term 4 gives \(4+3=7\), term 5 gives \(5+3=8\), so term 2 must carry the digit \(2+3=5\). Second, the position of that digit among the four characters follows \(4-|n-3|\), where n is the term number: term 1 gives \(4-|1-3|=2\), term 3 gives \(4-|3-3|=4\), term 4 gives \(4-|4-3|=3\), term 5 gives \(4-|5-3|=2\), so term 2 must place its digit at position \(4-|2-3|=3\). Combining both formulas, the missing term is the letters Q, R, T with the digit 5 inserted at position 3, that is Q, R, 5, T.

1. Option A (QTR7): uses digit 7, but the formula requires \(2+3=5\) for term 2, and it also reorders the letters to Q, T, R instead of the fixed Q, R, T sequence.
2. Option B (QR5T): the digit is 5, matching \(2+3=5\), and it sits at position 3, matching \(4-|2-3|=3\), both formulas are satisfied together with the letters kept in order.
3. Option C (RQ9T): starts with R instead of Q, breaking the fixed letter order, and its digit 9 does not equal \(2+3=5\).
4. Option D (TRQ6): scrambles the letter order to T, R, Q, and reuses digit 6, which the formula assigns to term 3, not term 2.

Only option B satisfies both the digit formula and the position formula for term 2.

Therefore, the correct answer is QR5T.