Quiz 4 on Analytical

Is w an integer? 
(1) 3w is an odd number.

(2) 2w is an even number.

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

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

• Both statements together are sufficient, but neither statement alone is sufficient. 

• Each statement alone is sufficient.

• Statement (1) & (2) together are not sufficient. 

If w, x, y, and z are the digits of a four-digit number N, a positive integer, what is the 

remainder when N is divided by 9? 

(1) w + x + y + z = 13 

(2) N + 5 is divisible by 9 

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

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

• Both statements together are sufficient, but neither statement alone is sufficient. 

• Each statement alone is sufficient.

• Statement (1) & (2) together are not sufficient. 

 A box contains only red balls, white balls, and blue balls. If a ball is randomly selected from 

the box, what is the probability that the ball will be either white or blue? 

(1) The probability that a ball will be blue is 1/5. 

(2) The probability that a ball will be red is 1/3.

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

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

• Both statements together are sufficient, but neither statement alone is sufficient. 

• Each statement alone is sufficient.

• Statement (1) & (2) together are not sufficient. 

A bucket was placed under a dripping tap which was dripping at a uniform rate. At what time 

was the bucket full? 

(1) The bucket was put in place at 2 P.M. 

(2) The bucket was half full at 6 P.M. and three-quarters full at 8 P.M. on the same day. 

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

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

• Both statements together are sufficient, but neither statement alone is sufficient. 

• Each statement alone is sufficient.

• Statement (1) & (2) together are not sufficient. 

If x and y are positive integers, is (x + y²)^1/3 an integer? 

(1) x = y² (y - 1) 

(2) x = 2 

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

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

• Both statements together are sufficient, but neither statement alone is sufficient. 

• Each statement alone is sufficient.

• Statement (1) & (2) together are not sufficient. 

A map representing countries R, S, W, X, Y, and Z is to be drawn. Adjacent countries cannot be the same color on the map. The only countries adjacent to each other are as follows: 

R, S, X, and Y are each adjacent to W. 

X is adjacent to Y. 

R and S are each adjacent to Z. 

Which of the following is a pair of countries that must be different in color from each other? 

• R and X

• S and X

• S and Z

• X and Z

• Y and Z

A map representing countries R, S, W, X, Y, and Z is to be drawn. Adjacent countries cannot be the same color on the map. The only countries adjacent to each other are as follows: 

R, S, X, and Y are each adjacent to W. 

X is adjacent to Y. 

R and S are each adjacent to Z. 

 If X is the same color as Z, then it must be true that- 

• R is the same color as Y. 

• S is the same color as X

• X is the same color as Y

• S is a different color from any other country

• W is a different color from any other country

A map representing countries R, S, W, X, Y, and Z is to be drawn. Adjacent countries cannot be the same color on the map. The only countries adjacent to each other are as follows: 

R, S, X, and Y are each adjacent to W. 

X is adjacent to Y. 

R and S are each adjacent to Z. 

Which of the following is a pair of countries that can be the same color as each other? 

• R and S

• S and W

• W and X

• W and Y

• X and Y

A map representing countries R, S, W, X, Y, and Z is to be drawn. Adjacent countries cannot be the same color on the map. The only countries adjacent to each other are as follows: 

R, S, X, and Y are each adjacent to W. 

X is adjacent to Y. 

R and S are each adjacent to Z. 

 Which of the following countries can be the same color as W?

• R

• S

• X

• Y

• Z

A map representing countries R, S, W, X, Y, and Z is to be drawn. Adjacent countries cannot be the same color on the map. The only countries adjacent to each other are as follows: 

R, S, X, and Y are each adjacent to W. 

X is adjacent to Y. 

R and S are each adjacent to Z. 

  If the fewest possible colors are used and one of the countries is the only one of a certain 

color, that country could be:

• W, but not any of the other countries 

• Z, but not any of the other countries 

• R or S, but not any of the other countries

• W or X or Y, but not any of the other countries

• W or Y or Z, but not any of the other countries