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(D) To find the number of pairs of letters in the word $GOLDEN$ that have the same number of letters between them as in the English alphabet,we check

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) To find the number of pairs of letters in the word $GOLDEN$ that have the same number of letters between them as in the English alphabet,we check both forward and backward directions:
$1$. Word: $G, O, L, D, E, N$
$2$. Alphabet positions: $G(7), O(15), L(12), D(4), E(5), N(14)$
$3$. Checking pairs:
- $G$ to $O$: $7$ to $15$ (Difference is $8$,letters between is $7$. In alphabet,$G$ and $O$ have $7$ letters between them: $H, I, J, K, L, M, N$. This is a match.)
- $G$ to $L$: $7$ to $12$ (Difference is $5$,letters between is $4$. In alphabet,$G$ and $L$ have $4$ letters between them: $H, I, J, K$. This is a match.)
- $D$ to $E$: $4$ to $5$ (Difference is $1$,letters between is $0$. In alphabet,$D$ and $E$ have $0$ letters between them. This is a match.)
- $L$ to $N$: $12$ to $14$ (Difference is $2$,letters between is $1$. In alphabet,$L$ and $N$ have $1$ letter between them: $M$. This is a match.)
There are $4$ such pairs $(G-O, G-L, D-E, L-N)$. The pair $E-N$ is not a match because in the alphabet,$E(5)$ and $N(14)$ have $8$ letters between them $(F, G, H, I, J, K, L, M)$,but in the word $GOLDEN$,$E$ and $N$ are adjacent,having $0$ letters between them. Thus,the correct count is $4$.

How many such pairs of letters are there in the word $GOLDEN$,each of which has as many letters between them in the word as in the English alphabet?

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