请教大家三道数学题，谢谢各位了

songchangwen

Q26:

If n is a positive integer, what is the value of n ?

(1)When n is divided by 3, the remainder is 2.

(2)When n² is divided by 3, the remainder is 1.



A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTHstatements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Q35:

In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party.She also received 10 percent of the votes cast by those voters registered with a political party.If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

A.0.06N + 3,200

B.0.1N + 7,200

C.0.4N + 7,200

D.0.1N + 8,000

E.0.06N + 8,000
Q28:

If n is a positive integer, what is the remainder when (7^{4n + 3})(6ⁿ) is divided by 10 ?

A.1

B.2

C.4

D.6

E.8

Q28:

If n is a positive integer, what is the remainder when (7^{4n + 3})(6ⁿ) is divided by 10 ?

A.1

B.2

C.4

D.6

E.8

wengyue31

额。。我只会做一题。。不知道对你有帮助么。
（1）单独显然无法确定是哪个正整数，反例：11,14
（2）单独也显然无法确定是哪个正整数，反例：11,14
如果（1）（2)同时成立也无法确定，反例：11，14。
所以我会选c。不过考试时候我会选放弃。。。

wengyue31

不对不对。。打错了，选e，都不正确

wengyue31

第二题是我同学做出来的。我是做不出的。
7的1次方各位是7 2次方各位是9 三次各位是3 四次 各位是1 五次各位是7 所以四次一个周期。取1代入，个位上就是3*（6^1)=18。除以10的余数就是8

sdcar2010

(7^(4n + 3))(6^n) = [7^(4n)][7^3][6^n]

The last digit of 6^n is always 6 itself (the other numbers who have this similar property is 0, 1, 5 )
Since we know that 7^2 = 49 and 9^2 = 81, we know that the last digit of 7^4 is 1.  Whenever you get a last digit of 1, the case becomes every simple.  In the above case, to get the last digit of the product, you simely calculate:
1 * 21 * 6 = [8]

sdcar2010

If n is a positive integer, what is the value of n ?

(1)When n is divided by 3, the remainder is 2.

(2)When n2 is divided by 3, the remainder is 1.

Let's cut to the chase and analyze if the combination of both conditions can give us a definite number n.

From (1), we know that (n + 1) mod 3 = 0.  From (2) we know that (n^2 - 1) mod 3 = 0. However, since (n^2 - 1) = (n + 1) * (n - 1), then based on condition (1) alone, we already know that (n^2 - 1) mod 3 = 0.  Therefore, condition 2 basically is a variation of condition 1.  Neither is sufficient.  Combined together is not sufficient, either.

sdcar2010

In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party.She also received 10 percent of the votes cast by those voters registered with a political party.If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

A.0.06N + 3,200

B.0.1N + 7,200

C.0.4N + 7,200

D.0.1N + 8,000

E.0.06N + 8,000

If 40 percent of the votes cast were cast by independent voters, then the rest 60% were cast by voters registered with a specific political party, of which 10% voted for Ms. Robbins.  0.6 N was the total number of voters registered witha specific political party. 0.06 N was the number of voters who registered with a party and voted for Ms. Robbins.  lus the 8000 vots from independent voters, the answer is 0.06 N + 8000.