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

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Manager
Joined: 16 Feb 2012
Posts: 178
Concentration: Finance, Economics
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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17 Aug 2013, 09:34
2
11
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25% (medium)

Question Stats:

81% (01:57) correct 19% (01:55) wrong based on 308 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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Joined: 14 Dec 2012
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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17 Aug 2013, 09:44
3
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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##### General Discussion
Senior Manager
Joined: 10 Jul 2013
Posts: 314
Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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17 Aug 2013, 09:51
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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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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10 Apr 2018, 10:44
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
Joined: 08 Sep 2016
Posts: 117
Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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10 Apr 2018, 13:40
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.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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10 Apr 2018, 17:54
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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Joined: 04 Sep 2016
Posts: 1249
Location: India
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Re: a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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10 Apr 2018, 18:26
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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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
a, b, c, and d are positive consecutive integers and a < b <  [#permalink]

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10 Apr 2018, 18:50
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
a, b, c, and d are positive consecutive integers and a < b < &nbs [#permalink] 10 Apr 2018, 18:50
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