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' $X$ ' is the product of all integers from 1 to 8 . If $X=2^a \cdot 3
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17 Apr 2025, 03:24
17 Apr 2025, 03:24
Expert Reply
00:00
Question Stats:
60% (00:59) correct
40% (01:44) wrong based on 25 sessions
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' $\(X\)$ ' is the product of all integers from 1 to 8 . If $\(X=2^a \cdot 3^b \cdot 5^c \cdot 7^d\)$, then $\(a+b+c+d=\)$ ?
(A) 9
(D) 12
(B) 10
(E) 13
(C) 11
(A) 9
(D) 12
(B) 10
(E) 13
(C) 11
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Re: ' $X$ ' is the product of all integers from 1 to 8 . If $X=2^a \cdot 3
[#permalink]
23 Apr 2025, 04:30
23 Apr 2025, 04:30
Expert Reply
$$
\(x=1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8=2^7 \times 3^2 \times 5 \times 7\) .
$$
Hence $\(a+b+c+d=7+2+1+1=11\)$.
Thus, the correct option is $C$.
\(x=1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8=2^7 \times 3^2 \times 5 \times 7\) .
$$
Hence $\(a+b+c+d=7+2+1+1=11\)$.
Thus, the correct option is $C$.
gmatclubot
Re: ' $X$ ' is the product of all integers from 1 to 8 . If $X=2^a \cdot 3 [#permalink]
23 Apr 2025, 04:30
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