If x is a positive integer, is x3- 3x2 + 2x divisible by 4?
(1) x = 4y + 4, where y is an integer
(2) x = 2z + 2, where z is an integer
(1) x = 4y + 4, where y is an integer
(2) x = 2z + 2, where z is an integer
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
RedeemTarget Test Prep · GMAT
Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

with Chris Peckover, 100th-Percentile GMAT Scorer
Self-paced EA prep. Study on your schedule.

with Logan Thompson
Complete access from day one. Study on your schedule.
Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.
Target question: Is x^3- 3x^2 + 2x divisible by 4?'manpreet singh wrote:If x is a positive integer, is x^3- 3x^2 + 2x divisible by 4?
(1) x = 4y + 4, where y is an integer
(2) x = 2z + 2, where z is an integer
Brent@GMATPrepNow wrote:Hey Brent,'manpreet singh wrote:If x is a positive integer, is x^3- 3x^2 + 2x divisible by 4?
Onto the statements.
Given: x = 4y + 4, where y is an integer
Factor to get: x = 4(y + 1)
This tells us that x is divisible by 4, which means x is even
If x is even, then (according to my point in green above) (x-2)(x-1)(x) must be divisible by 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
A quick one. Since the above bold says that x is divisible by 4, doesnt that already mean that a product of x and any other numbers will also be divisible by 4. It's just overcomplicating things a wee bit when we have to look at the series and then conclude that x-2 is also even.
anuprajan5 wrote:Ah, you're totally right! I kind of took a step backwards there, didn't I?Brent@GMATPrepNow wrote:Hey Brent,'manpreet singh wrote:If x is a positive integer, is x^3- 3x^2 + 2x divisible by 4?
Onto the statements.
Given: x = 4y + 4, where y is an integer
Factor to get: x = 4(y + 1)
This tells us that x is divisible by 4, which means x is even
If x is even, then (according to my point in green above) (x-2)(x-1)(x) must be divisible by 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
A quick one. Since the above bold says that x is divisible by 4, doesnt that already mean that a product of x and any other numbers will also be divisible by 4. It's just overcomplicating things a wee bit when we have to look at the series and then conclude that x-2 is also even.
In fact, earlier in the solution, I said that the product of 3 consecutive integers be divisible by 4 if one of the 3 integers is divisible by 4. Then, after I learn that one of the integers is divisible by 4, I take the longer/slower approach to reach the same conclusion.
Good catch!
Cheers,
Brent
New here Create free account