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# If p is the product of the reciprocals of integers from 150 to 250, in

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Re: If p is the product of the reciprocals of integers from 150 to 250, in [#permalink]
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Well p is product of reciprocals from 150 to 250 and

q is product of reciprocals from 150 to 251
So we can say that

q= p*1/251
Anvesh99

Hope this helps..

Anvesh99 wrote:
Archit3110 wrote:
we can write q = p*(1/251)
1/p+1/q ; 1/p + 251/p
252/p
option D

Bunuel wrote:
If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product of the reciprocals of integers from 150 to 251, inclusive, what is the value of $$(p^{−1} + q^{−1})$$ in terms of p?

(A) p/(251)^2

(B) 251*252*p

(C) 252p

(D) 252/p

(E) 251*252*p^2

Hi Archit3110

Can you please explain your answer. How did you get the q = p*(1/251). I think I did not get the question quite well.

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If p is the product of the reciprocals of integers from 150 to 250, in [#permalink]
Anvesh99 wrote:
Archit3110 wrote:
we can write q = p*(1/251)
1/p+1/q ; 1/p + 251/p
252/p
option D

Bunuel wrote:
If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product of the reciprocals of integers from 150 to 251, inclusive, what is the value of $$(p^{−1} + q^{−1})$$ in terms of p?

(A) p/(251)^2

(B) 251*252*p

(C) 252p

(D) 252/p

(E) 251*252*p^2

Hi Archit3110

Can you please explain your answer. How did you get the q = p*(1/251). I think I did not get the question quite well.

p = (1/150)*(1/151)*(1/152).......................*(1/249)*(1/250).
q= (1/150)*(1/151)*(1/152).......................*(1/249)*(1/250)*(1/251)

Replacing (1/150)...........(1/250) with p
q = p * (1/251)

-> (1/p)+ (1/(p * (1/251)))
-> (1/p)+(251/p)
-> 252/p -> Option D
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Re: If p is the product of the reciprocals of integers from 150 to 250, in [#permalink]
Bunuel wrote:
If p is the product of the reciprocals of integers from 150 to 250, inclusive, and q is the product of the reciprocals of integers from 150 to 251, inclusive, what is the value of $$(p^{−1} + q^{−1})$$ in terms of p?

(A) p/(251)^2

(B) 251*252*p

(C) 252p

(D) 252/p

(E) 251*252*p^2

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Solution:

We are given $$p=\frac{1}{150}\times \frac{1}{151}\times \frac{1}{152}\times .......\times \frac{1}{249}\times \frac{1}{250}$$

And $$q=\frac{1}{150}\times \frac{1}{151}\times \frac{1}{152}\times .......\times \frac{1}{249}\times \frac{1}{250}\times \frac{1}{251}$$

Or we can write $$q=p\times \frac{1}{251}$$

$$⇒q=\frac{p}{251}$$......$$(i)$$

We need the value $$(p^{−1} + q^{−1})$$

$$=\frac{1}{p}+\frac{1}{q}$$

$$=\frac{1}{p}+\frac{251}{p}$$

$$=\frac{252}{p}$$

Hence the right answer is Option D
Re: If p is the product of the reciprocals of integers from 150 to 250, in [#permalink]
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