[求助]PREP17,44,73,86,173

17.   1329-!-item-!-187;#058&000662

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives.  Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1)  One of the six countries sent 41 representatives to the congress.

(2)  Country A sent fewer than 12 representatives to the congress.

44.   3852-!-item-!-187;#058&003578

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

(1) a + b = -1

(2) The graph intersects the y-axis at (0, -6).

73.   6279-!-item-!-187;#058&004943

What is the average (arithmetic mean) of eleven consecutive integers?

(1)  The average of the first nine integers is 7.

(2)  The average of the last nine integers is 9.

86.   7767-!-item-!-187;#058&005660

Each of the students in a certain class received a single grade of P, F, or I.  What percent of the students in the class were females?

(1)  Of those who received a P, 40 percent were females.

(2)  Of those who received either an F or I, 80 percent were males

173.
                                            17281-!-item-!-187;#058&011070

If N is a positive integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N.

(2) N = (2^5)(3^2)(5^7)(7^6)

73.   6279-!-item-!-187;#058&004943

What is the average (arithmetic mean) of eleven consecutive integers?

(1)  The average of the first nine integers is 7.

(2)  The average of the last nine integers is 9.

86.   7767-!-item-!-187;#058&005660

Each of the students in a certain class received a single grade of P, F, or I.  What percent of the students in the class were females?

(1)  Of those who received a P, 40 percent were females.

(2)  Of those who received either an F or I, 80 percent were males

173.
                                17281-!-item-!-187;#058&011070

If N is a positive integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N.

(2) N = (2^5)(3^2)(5^7)(7^6)

44.   3852-!-item-!-187;#058&003578

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

(1) a + b = -1

(2) The graph intersects the y-axis at (0, -6).

73.   6279-!-item-!-187;#058&004943

What is the average (arithmetic mean) of eleven consecutive integers?

(1)  The average of the first nine integers is 7.

(2)  The average of the last nine integers is 9.

86.   7767-!-item-!-187;#058&005660

Each of the students in a certain class received a single grade of P, F, or I.  What percent of the students in the class were females?

(1)  Of those who received a P, 40 percent were females.

(2)  Of those who received either an F or I, 80 percent were males

173.
                            17281-!-item-!-187;#058&011070

If N is a positive integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N.

(2) N = (2^5)(3^2)(5^7)(7^6)

73.   6279-!-item-!-187;#058&004943

What is the average (arithmetic mean) of eleven consecutive integers?

(1)  The average of the first nine integers is 7.

(2)  The average of the last nine integers is 9.

86.   7767-!-item-!-187;#058&005660

Each of the students in a certain class received a single grade of P, F, or I.  What percent of the students in the class were females?

(1)  Of those who received a P, 40 percent were females.

(2)  Of those who received either an F or I, 80 percent were males

173.
                17281-!-item-!-187;#058&011070

If N is a positive integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N.

(2) N = (2^5)(3^2)(5^7)(7^6)

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives.  Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1)  One of the six countries sent 41 representatives to the congress.

(2)  Country A sent fewer than 12 representatives to the congress.

  Solution:

I think we need to know that reps of A < B < C < D < E, otherwise the answer is E.

Work:
Did A send at least 10 reps?

A+B+C+D+E=75
Statement 1:
1 country sent 41 representatives

A+B+C+D=34
possibility:
1+2+3+28=34
insufficient, A could either be 1 or 28

Statement 2:
Country A sent fewer than 12 representatives to the congress
A=11, B+C+D+E=64, which is possible
A=9, B+C+D+E=66, which is possible
insufficient

Statements 1&2:
A+B+C+D=34
A=11, B+C+D+E=23
1+2+3+17=23, so A can be 11
A=9, B+C+D+E=25
1+2+3+19, so A can be 13
still insufficient
E

(1) a + b = -1

(2) The graph intersects the y-axis at (0, -6).

Solution:

Stem1:
To intersect with x - axis y =0
So, (x +a)(x +b)=0
Hence x = -a or x = -b (points of intersection). But we don’t know the value of a and b. NOT SUFF.

St 2 says interection with y - axis at (0,6)
Hence 6 = (0 +a)(0 +b)
ab = 6
a + b = -1
Solve the 2 to get a and b 

What is the average (arithmetic mean) of eleven consecutive integers?

(1)  The average of the first nine integers is 7.

(2)  The average of the last nine integers is 9.

 Stem1:

Le the numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8.

So, x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8=63

=> 9x=63-36

=>x=27/9=3.

So, the numbers are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. SUFF.

Stem2:

Let the biggest number is x,

Others are x-1, ………………x-8.

Now, x+x-1+……………x-8=81

=>9x-36=81

=>x=117/9=13.

We can have the average. SUFF.

Answer is D.

The common multiple of 14 and 35 is 70. [2×5×7=70.]

Since unit digit is zero, whatever may be other factors the unit digit again will be zero. SUFF.

Stem2:

N=10× (2^4)(3^2)(5^6)(7^6)

So, the multiplication will result a number that has unit digit zero. SUFF.

Answer is D.
                            

Stem1:

The common multiple of 14 and 35 is 70. [2×5×7=70.]

Since unit digit is zero, whatever may be other factors the unit digit again will be zero. SUFF.

Stem2:

N=10× (2^4)(3^2)(5^6)(7^6)

So, the multiplication will result a number that has unit digit zero. SUFF.

Answer is D.
                    

Excellent explanation by bth.

多谢 bth.