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I looked at a few modular arithmetic websites and I'm a neophyte when it comes to the legal operations/rules, syntax, and procedures of modular arithmetic. No GRE guide I've seen talks about modular arithmetic (not even the official one!).
Following are five relevant questions from my GRE coaching website (which only gives answers with no explanation).
Trial-and-error is always an option but I'm looking for a systematic approach, clear, efficient step-by-step procedure, which gives me confidence to tackle such problems.
How do I set up the congruent modulo expression?
What operations are allowed in that expression, and which one's are usually performed to reach answers to the below questions with this approach?
Following are five relevant questions from my GRE coaching website (which only gives answers with no explanation).
Trial-and-error is always an option but I'm looking for a systematic approach, clear, efficient step-by-step procedure, which gives me confidence to tackle such problems.
How do I set up the congruent modulo expression?
What operations are allowed in that expression, and which one's are usually performed to reach answers to the below questions with this approach?
GRE Website said:x and y are positive integers, where x is a multiple of 3 and [tex]x*y[/tex] is a multiple of 13. The remainder of [tex]y/9[/tex] is R.
Col A: R
Col B: 1
R is the remainder of (10^32 + 2)/11.
Col A: R
Col B: 3
[tex]3 + 3^2 + 3^3[/tex] + ……… + [tex]3^x[/tex]. What is the first value of x at which the sum will be divisible by 6?
[tex]A. 15[/tex]
[tex]B. 19[/tex]
[tex]C. 21[/tex]
[tex]D. 28[/tex]
[tex]E. 53[/tex]
5 is the remainder of [tex]x/6[/tex] and 3 is the remainder of [tex]x/5[/tex].
Col A: The least possible value of x
Col B: 23
If [tex]y = -(x-1)[/tex], then what is the value of 1/3(mod(y+x))?
x a positive integer and y is an odd positive integer
Find the remainder when (x+1)*(y+2) is divided by 7
Positive integer Z_1 divided by 7 gives a remainder of 5 and Z_2 divided by 4 leaves a remainder of 3. Some constraint on Z_1 and Z_2 (e.g., they are equal and should be minimum [e.g., Z_1 = Z_2, min(Z_1)], or Z_2 is a defined in terms of Z_1 [e.g., Z_2 = Z_1 +2]).
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