Three Dice, Each with Faces Numbered 1 through 6, Were Tossed GMAT Data Sufficiency

Question: Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the sum of the numbers that turned up on all three dice?

1. The sum of two of the number that turned up was 10
2. The sum of two of the numbers that turned up was 11

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Solution and Explanation:

Approach Solution (1):

1. The sum of the two of the numbers that turned up was 10. The sum can be 4 + (5 + 5) = 14 or (4 + 6) + any > 10

Not sufficient

2. The sum of two of the numbers that turned up was 11: x + y = 11: The first dice turned up 4, so it can be neither x nor y (because the other one will be 7, so more than 6). Thus the sum is 4 + (x + y) = 15

Sufficient

Correct Option: B

Approach Solution (2):

Let there be three numbers D1, D2, and D3
D1 = 4

There are two possibilities for S1
(5,5, 4) and (4, 6, anything)

If D1 = 4 and D2 = 6 then D3 can be anything and we cannot find the sum
Hence S1 is insufficient

For S2, there is only one combination for making 11 i.e. (4, 5, 6)
Here we have two combinations

1. D1 = 4 D2 = 5 D3 = 6
2. D1 = 4 D2 = 6 D3 = 5

But since in both the cases the sum is 15… hence the statement 2 is sufficient

Correct Option: B

Approach Solution (3):

S1: The sum of two of the numbers that turned up was 10
This statement is not sufficient because we cannot determine whether the 4 we already know about is among those two dice

Case a: The two dice that add to 10 are 5 and 5, and the other die is the 4. In this case, the answer to the target question is the sum = 5 + 5 + 4 = 14
Case b: The two dice that add to 10 are 6 and 4, and the other die is a 1. In this case, the answer to the target question with certainty, S1 is not sufficient

S2: The sum of two of the numbers that turned up was 11
This statement doesn’t have the same issue that S1 had.
Since the sum of the two mentioned dice is 11, we can be certain that those two dice are 5, and 6, since those are the only two possible values that will add to 11.
This means the three dice are 5, 6, and 4
So, the answer to the target question is the sum = 5 + 6 + 4 = 15

Since we can answer the target question with certainty, S2 is sufficient

Correct Option: B

“Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the sum of the numbers that turned up on all three dice?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Suggested GMAT Data Sufficiency Samples

• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• If ab = ac is b = 2?​ GMAT Data Sufficiency 
• What is the value of \(6x^2+9y^2\)? GMAT Data Sufficiency
• Buster Leaves the Trailer at Noon and Walks Towards the Studio GMAT Data Sufficiency 
• If 53 Students are Enrolled in Both the CS103 (Algorithms and Data Structures) And M101 (Mathematics for Computer Science) Classes, How Many of the CS103 Students are no Enrolled in M101? GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even? GMAT Data Sufficiency
• Is the Area of the Triangle ABC Greater than the Area of the Triangle DEF? GMAT Data Sufficiency
• If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
• The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?, GMAT Data Sufficiency
• If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
• If There are 78 People Working at an Office, How Many of Them are Women Older than 40?, GMAT Data Sufficiency
• If√3+√x−1=4, what is the value of x? GMAT Data Sufficiency 
• If ab = ac is b = 2? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Data Sufficiency
• Is the positive integer n a multiple of 24? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• Is |x-10| > |x-30| GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Do The Diagonals Of A Quadrilateral ABCD Bisect Each Other GMAT Data Sufficiency
• A Certain Truck Uses \(\frac{1}{12} +kv^2\) Gallons of Fuel Per Mile GMAT Data Sufficiency
• Is c^(abcd) = 1? (1) |a|>|b|>|c|>|d| (2) c^d>3 GMAT Data Sufficiency
• If x is an integer, can the number (5/28)(3.02)(90%)(x) be GMAT Data Sufficiency
• On Sunday Morning, a Printing Press Printed its Newspapers at a GMAT Data Sufficiency
• Is Quadrilateral ABCD A Rhombus? GMAT Data Sufficiency
• What Is The Volume Of Rectangular Box R? GMAT Data Sufficiency
• Does the curve \((x-a)^2+(y-b)^2=16\) intersect the Y-axis? GMAT Data Sufficiency
• Does The Graphical Representation Of The Quadratic Function GMAT Data Sufficiency
• If X = 0.rstu, Where r, s, t, And u Each Represent A Nonzero Digit GMAT Data Sufficiency
• GMAT Data Sufficiency-Is \(\frac{7^7}{7^x}\) an integer?
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
• What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency