Test: Data Sufficiency - 1 - GMAT MCQ

Let A represent the cost of a type A football and B the cost of a type B football. From the problem, we know:

• The total cost of one type A and one type B football is $500.
• From statement 1, the cost of type B football is $200.

Using statement 1:

• Since B = $200, we can find A:
• A = $500 - B = $500 - $200 = $300.
• Thus, the cost of two type A footballs is 2A = $600.

Now, using statement 2:

• From statement 2, we have 2A + 3B = $1200.
• Substituting B = $200 into the equation:
• 2A + 3(200) = 1200.
• This simplifies to 2A + 600 = 1200.
• Subtracting 600 from both sides gives 2A = $600, hence A = $300.

Both statements are sufficient to determine the price of two type A footballs, which is $600.

In statement 1, since one of the divisors is 7, it indicates that the number is a multiple of 7. This means there are infinitely many possibilities, making the statement insufficient.

In statement 2, the number is said to be divisible by only two numbers. This suggests that p is a prime number, as prime numbers have exactly two positive divisors. Since there are infinitely many prime numbers, this statement is also insufficient.

When we combine both statements:

• p is a prime number and is divisible by 7.
• This leads us to conclude that p must be 7.

Thus, both statements together are sufficient to answer the question, while neither statement alone is sufficient.

Deposit (P) = 3000.

The accumulated amount can be calculated using the following formulas:

• For compound interest: Accumulated amount = P (1 + r/100)ⁿ
• For simple interest: Accumulated amount = P + (P × r/100 × n)

In Statement 1:

• r = 4.3
• P = 3000
• However, the value of n is not provided, making it insufficient.
• Additionally, the type of interest is not specified.

In Statement 2:

• n = 5
• P = 3000
• But the value of r is missing, rendering it insufficient as well.
• Again, the type of interest is not disclosed.

When combining both statements:

• P = 3000, r = 4.3, and n = 5 are known.
• Yet, without knowing the specific type of interest, we cannot accurately apply the formulas.

Therefore, Statements (1) and (2) TOGETHER are NOT sufficient to determine the accumulated amount.

Volume = length × width × height

From the statements provided:

• Statement 1: Let the width be x. Then, the length is 2x and the height is 4 inches.
• The volume can be calculated as: Volume = x × 2x × 4 = 8x² cubic inches. Since this expression depends on x, it is insufficient on its own.

• Statement 2: The length is 6 inches, but the width and height are unknown, making it insufficient to determine the volume.

When we combine both statements:

• From statement 2, we have length = 6 inches.
• From statement 1, we set 2x = 6, which gives x = 3 inches.
• This means the width is 3 inches and the height is 4 inches.
• Now, we can calculate the volume: Volume = 3 × 4 × 6 = 72 cubic inches.

Therefore, BOTH statements TOGETHER are sufficient to determine the volume, but NEITHER statement ALONE is sufficient.

4r + 2t = 14

Let's evaluate the statements:

• Statement 1: If t = 2, substituting this value into the equation:
• 4r + 2(2) = 14
• 4r + 4 = 14
• 4r = 10
• r = 2.5
• This statement is sufficient to find the value of r.

• Statement 2: Here, we know r > t, but no numeric values are provided.
• This means that the value of r could be any number greater than t, leading to multiple possible values for r.
• Therefore, this statement is not sufficient.

Thus, only Statement 1 is sufficient to determine the value of r.

a_n = a + (n - 1)d

In statement 1, the third term is given as:

• a₃ = a + (3 - 1)d = 1.428
• This simplifies to: a + 2d = 1.428

As this provides only one equation with two unknowns, we cannot determine the value of d. Thus, this statement is not sufficient.

In statement 2, we know:

• a = 1
• a₅ = a + (5 - 1)d = 1.856
• Substituting for a gives: 1 + 4d = 1.856
• This leads to: d = 0.214

The common difference is 0.214, making this statement sufficient.

Cost price is $80, which represents 100%.

• Statement 1: Profit is 30%.
• Calculate profit:
  • Profit = 30% of $80 = $24.
• Using the selling price:
  • Profit = Selling Price - Cost Price = $104 - $80 = $24.
• Thus, Statement 1 is sufficient.

• Statement 2: Selling price is $104.
• Calculate profit:
  • Profit = Selling Price - Cost Price = $104 - $80 = $24.
• Therefore, Statement 2 is also sufficient.

Since each statement alone is sufficient, the answer is D.

Ratio of water to alcohol: 2:5.

In a 14-cup container:

• Water = 2/7 x 14 = 4 cups.
• Alcohol = 14 - 4 = 10 cups.

When water is increased by 14%:

• New volume of water = 114/100 x 4 = 4.56 cups.
• New total volume of the liquid = 10 + 4.56 = 14.56 cups.

Thus, statement 1 is sufficient.

Regarding statement 2:

• The ratio of water to alcohol is 4:5.
• However, the quantity of the liquid added or the specific amounts of water and alcohol are not provided.
• Therefore, statement 2 is not sufficient.

In statement 1, the linear scale factor of triangle A to triangle B is 7 : 10. This means the area scale factor is 49 : 100. However, as we do not have the area of triangle B, we cannot calculate the area of triangle A. Therefore, this statement is insufficient.

In statement 2, we know that triangle B is larger than triangle A, which indicates that the ratio of B to A is greater than 1. Without additional information about the ratio or the area of either triangle, this statement alone is also insufficient.

When we combine both statements, the area scale factor remains 49 : 100, where 49 represents the smaller triangle (A) and 100 represents the larger triangle (B). However, since we still lack the area of triangle B, we cannot determine the area of triangle A. Thus, even together, the statements are insufficient.

Let cost of pen = P, pencil = Q.
From (1): 3P + 2Q = 80 — (i)
From (2): 2P + 2Q = 70 and Q = 10
Substitute Q = 10 into both equations:
From (2): 2P + 20 = 70 → 2P = 50 → P = 25
From (1): 3P + 20 = 80 → 3P = 60 → P = 20
Conflict in values shows contradiction → So both are needed to cross-verify.