If a, b, c are three consecutive integers such that c b a and abc

Question

If a, b, c are three consecutive integers such that c > b > a and abc = 3360. What is the value of b?

A. 13
B. 14
C. 15
D. 16
E. 17

doomedcat · Answer

factorize 3360 we get = 2*2*2*2*2*5*3*7
given a*b*c are consecutive
A) 13 not possible
B) 14 , it can be 13 14 15 ; 13 not possible so eliminate B
C) 15, abc would be 14 15 16; possible

C

KSBGC · Answer

prime factorize:

3360 = 3*5*2*2*2*2*7*2

3*5 =15
 2^4= 16 
7*2 =14

C is the correct answer.

Archit3110 · Answer

3360 = 14*15*16

b would be 15 IMO C

Abhishek009 · Answer

3360 = 14*15*16

So,  c = 16  ,  b = 15  &  a = 14

Thus, Answer must be (C) 15

luisdicampo · Answer

Given that  a, b, c  are three consecutive integers and  abc = 3360 .
Since the integers are consecutive, their values are very close to each other. Therefore, the product  a 	imes b 	imes c  will be approximately equal to the cube of the middle term ( b^3 ).

Method 1: Approximation (Fastest) 
We need to find  b  such that  b^3 \approx 3360 .

Let's look at perfect cubes we might know:
 10^3 = 1000  (Too small)
 20^3 = 8000  (Too big)

Let's check the midpoint, 15:
 15^3 = 3375

The given value (3360) is extremely close to 3375.
This suggests the middle term  b  is 15.

Let's verify with the integers centered around 15:  14, 15, 16 .
 14 	imes 15 	imes 16 
 = 210 	imes 16 
 = 3360 
This matches exactly.

Method 2: Prime Factorization 
If the approximation isn't immediately obvious, break 3360 into prime factors to find three consecutive numbers.

3360 = 10 	imes 336 
 = 2 	imes 5 	imes 3 	imes 112 
 = 2 	imes 5 	imes 3 	imes 2 	imes 56 
 = 2^2 	imes 3 	imes 5 	imes 7 	imes 8 
 = 2^5 	imes 3 	imes 5 	imes 7

Now, group these factors to form three consecutive integers:
1. We see a  5  and a  3 .  5 	imes 3 = 15 .
2. We see a  7  and a  2 .  7 	imes 2 = 14 .
3. The remaining factors are four  2 's ( 2^4 ).  16 .

The integers are 14, 15, and 16.
Since  c > b > a ,  b  is the middle integer.
 b = 15 .

Answer: C

If a, b, c are three consecutive integers such that c > b > a and abc

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