Q. If the LCM of two numbers is 60 and their HCF is 5, what is the sum of the two numbers if they are both less than 30? (2023)
A.
25
B.
35
C.
40
D.
30
Solution
Let the two numbers be 5a and 5b. Then, LCM(5a, 5b) = 5 * LCM(a, b) = 60, which gives LCM(a, b) = 12. The pairs (3, 4) work, giving numbers 15 and 20, which sum to 35.
Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
A.
It is 216.
B.
It is 72.
C.
It is 36.
D.
It is 6.
Solution
The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
A.
It is 720.
B.
It is 60.
C.
It is 12.
D.
It is 5.
Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
A.
(5, 12)
B.
(10, 30)
C.
(15, 20)
D.
(5, 15)
Solution
The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.
Q. If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?
A.
8% increase
B.
10% decrease
C.
12% increase
D.
2% decrease
Solution
Let the original length be L and width be W. The new length is 1.2L and the new width is 0.9W. The original area is LW and the new area is (1.2L)(0.9W) = 1.08LW. The percentage change in area is ((1.08LW - LW) / LW) * 100 = 8% increase.
Q. If the letters A, B, C, D, and E are arranged in a straight line such that A is to the left of B, C is to the right of D, and E is to the right of A, which of the following must be true?
A.
B is to the right of D
B.
C is to the left of E
C.
A is to the left of C
D.
D is to the left of E
Solution
Since A is to the left of B and E is to the right of A, it follows that A must be to the left of C.
Q. If the line graph indicates a steady decline in sales for Product C from January to June, what can be inferred about the market trend for that product?
A.
Increased competition
B.
Seasonal demand
C.
Improved marketing
D.
Product quality issues
Solution
The steady decline suggests increased competition in the market affecting Product C's sales.
Q. If the line graph indicates a steady decline in the sales of Product C from January to June, what can be inferred about the market trend for that product?
A.
Increased competition
B.
Seasonal demand
C.
Improved marketing
D.
Consumer preference shift
Solution
The steady decline suggests increased competition affecting Product C's sales.
