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
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.
Well, this isn't a real GMAT question. I'd use modular arithmetic, which you don't need for the GMAT. By ~, I mean 'congruent to' (if anyone reading this doesn't know what that means, don't worry about it!).sudhir3127 wrote:Find the remainder of
(2222^5555 + 5555^7777)/7
Answer will follow soon....
How is 2222 congruent to 3 mod 7 and 5555 congruent to 4 mod 7? What does congruent mean in this context ? I am totally lost ....Ian Stewart wrote:Well, this isn't a real GMAT question. I'd use modular arithmetic, which you don't need for the GMAT. By ~, I mean 'congruent to' (if anyone reading this doesn't know what that means, don't worry about it!).sudhir3127 wrote:Find the remainder of
(2222^5555 + 5555^7777)/7
Answer will follow soon....
2222 ~ 3 mod 7
2222^5555 ~ 3^5555 mod 7
3^5555 = (3^2)*(3^5553) = (3^2)*[(3^3)^1851]
Since 3^3 = 27 ~ -1 mod 7, we have
(3^2)*[(3^3)^1851] ~ 2*(-1)^1851 mod 7 ~ -2 mod 7 ~ 5 mod 7.
So the remainder is 5 when 2222^5555 is divided by 7.
Similarly for 5555^7777:
5555 ~ 4 mod 7
4^7777 = 4 * 4^7776 = 4 * (4^3)^2592 ~ 4 * 1^2592 mod 7 ~ 4 mod 7.
(here, using that 4^3 ~ 1 mod 7).
So
(2222^5555 + 5555^7777) ~ 4+ 5 mod 7 ~ 2 mod 7.
The remainder should be 2, unless I've made an arithmetic mistake, which wouldn't surprise me, considering how quickly I'm doing this.
As I said above, you don't need any of this for the GMAT. 'Congruent to' means 'has the same remainder as', and when you learn 'modular arithmetic', you learn how to do arithmetic with remainders -that's all I was doing above. Still, if you're preparing for the GMAT, you don't need to worry about any of this.acecoolan wrote: How is 2222 congruent to 3 mod 7 and 5555 congruent to 4 mod 7? What does congruent mean in this context ? I am totally lost ....
New here Create free account
