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Manager  Joined: 16 Feb 2012
Posts: 147
Concentration: Finance, Economics
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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Question Stats: 82% (01:59) correct 18% (02:00) wrong based on 248 sessions

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a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

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Director  Joined: 14 Dec 2012
Posts: 703
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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5
2
Stiv wrote:
a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

a, b, c, and d are positive consecutive integers

since a b c d are consecutive integers
therefore
$$d= a+3$$

now given
$$2abc = bcd$$
$$bc(2a-d) = 0$$
since they are positive hence bc cant be equal to 0
therefore $$2a-d = 0$$
putting $$d = a+3$$
$$2a-a-3=0.$$
$$a=3$$
therefore $$b= 4 and c= 5$$
hence bc = $$4*5 = 20$$
HENCE D
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Senior Manager  Joined: 10 Jul 2013
Posts: 289
Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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Stiv wrote:
a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

Here, bcd = 2 abc
, so, d = 2a

and we know, a<b<c<d
so the series is like, 3<4<5<6
Finally, bc = 4 × 5 = 20
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Asif vai.....
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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Bunuel niks18 chetan2u

Quote:
a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

My sol matched with blueseas let me know if there is any better approach?
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Manager  B
Joined: 08 Sep 2016
Posts: 102
Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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Asifpirlo wrote:
Stiv wrote:
a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

Here, bcd = 2 abc
, so, d = 2a

and we know, a<b<c<d
so the series is like, 3<4<5<6
Finally, bc = 4 × 5 = 20

I did the problem this way and got the correct answer, but I think the primary reason why this approach worked is because we are told that the variables were positive integers. I don't think this approach would have worked if the sign wasn't mentioned.
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Joined: 25 Feb 2013
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Location: India
GPA: 3.82
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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Bunuel niks18 chetan2u

Quote:
a, b, c, and d are positive consecutive integers and a < b < c < d. If the product of b, c, and d is twice that of a, b, and c, then bc =
A 2
B 6
C 12
D 20
E 30

My sol matched with blueseas let me know if there is any better approach?

I am not sure about "Better" but yes there are other approaches to solve the problem.

Now it is also given that $$2abc=bcd =>d=2a$$.

You can work backwards through options -

2=1*2, hence b=1,c=2,d=3 and a=0, which is not possible as a is positive.

6=2*3, hence b=2,c=3,d=4 and a=1, but d=2a, Hence ignore

12=3*4, hence b=3,c=4,d=5 and a=2, again not possible

20=4*5, hence b=4, c=5, d=6 and a=3. here d=2a. Hence our answer

30=5*6, hence b=5,c=6,d=7 and a=4, which is not possible
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Posts: 1366
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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1
niks18

Quote:
By looking at the answer choices, you should realize that both$$b$$ & $$d$$ has to be Even.

Can you verify highlighted text again?
Fundamentally, EITHER of two numbers is suff for product to be EVEN.

Is your rationale based on the fact that a,b,c,d are consecutive integers?
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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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niks18

Quote:
By looking at the answer choices, you should realize that both$$b$$ & $$d$$ has to be Even.

Can you verify highlighted text again?
Fundamentally, EITHER of two numbers is suff for product to be EVEN.

Is your rationale based on the fact that a,b,c,d are consecutive integers?

My bad, I read the question as b*d instead of b*c. Yes you are correct, in your observation. I have edited my solution
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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_________________ Re: a, b, c, and d are positive consecutive integers and a < b <   [#permalink] 11 Apr 2019, 16:14
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