Question: Crowan throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt. What is the probability that the result of any attempt is an odd integer divisible by 25?

1. 7/216
2. 5/91
3. 13/88
4. 1/5
5. 3/8

Answer: A

Solution and Explanation

Approach Solution 1:

The total number of ways to throw 3 dice is 6 x 6 x 6 = 216

Only if two of the numbers are both 5s and the third number is an odd number can the product of the numbers on the top of three dice be an odd number that is divisible by 25. Well, here we are:
{1, 5, 5}, {5, 1, 5}, {5, 5, 1}, {3, 5, 5}, {5, 3, 5}, {5, 5, 3} and {5, 5, 5}
Thus the probability is 7/216.

Hence the correct answer is A.

Approach Solution 2:

As 555 can only happen in one manner in this situation, the nominator will have the following values:

551 - 515 - 155;
553 - 535 - 355;

555.

P(55O)= 7/216 (if you want to calculate as in previous case then:
P(55O)=P(551)+P(553)+P(555)=3!/2!∗1/6∗1/6∗1/6+3!/2!∗1/6∗1/6∗1/6+1/6∗1/6∗1/6=7/216)

Notice that the 16 scenarios listed above include all situations in which there are at least two 5s on a roll of three dice: 7 of these situations result in an odd sum, and 9 of them in an even amount.

Hence the correct answer is A.

Approach Solution 3:

The following strategy would be simpler
The number must contain the digit 25 in order to be a multiple of 25.
Thus, let there be three dashes:
Fix the first two dashes for 25, which is 5*5, which may be done in a variety of ways, including 1*1 = 1.
Let's insert the odd integers other than 5 in the last dash; the number of possible methods would be 2.
This arrangement's total permutations would be (1*1*2)*3!/2! (we must divide by 2! because two 5s are the same).
The likelihood of this is 6/216.
Probability of 555 = 1/16
As a result, the total problem of 7/216

Hence the correct answer is A.

“Crowan throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt.” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Suggested GMAT Problem Solving Samples

• Metropolis Corporation has 4 Shareholders GMAT Problem Solving
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• A farm has chickens, cows and sheep GMAT Problem Solving
• How many Terminating Zeroes does 200! Have? GMAT Problem Solving
• 1511−151014=? GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If 298=256L+N298=256L+N , Where L and N are Integers and 0≤N≤40≤N≤4 , What is the Value of N? GMAT Problem Solving
• How Many 5-Letter Words can be Formed Using the Letters of the English Alphabet that Contain 2 Different Vowels GMAT Problem Solving
• If a+b+c = 0 and a^3+b^3+c^3 = 216, What is the Value of a∗b∗c ? GMAT Problem Solving
• If a Polygon has 44 Diagonals, Then How Many Sides are There in the Polygon? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), For Every n≥1, Then a11 Equals GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• A Container in the Shape of a Right Circular Cylinder is 1/2 Full of Water. GMAT Problem Solving
• How Many Multiples of 7 are there Between 21 and 343, Exclusive? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ? GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• The Figure Shown Above Consists of a Shaded 9-Sided Polygon GMAT Problem Solving
• A list of measurements in increasing order is 4, 5, 6, 8, 10 and x GMAT Problem Solving
• Rahul Can Finish a Job in 30 Days GMAT Problem Solving
• The Price of Raw Materials Has Gone up by 15% GMAT Problem Solving
• In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics, GMAT Problem Solving
• If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
• Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
• Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
• If n = 3, What is The Value of 2^2n+1? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• The Volume of a Sphere With Radius r is (4/3)*pi*r^3 and the Surface Area is 4*pi*r^2 GMAT Problem Solving
• Which of the Following is Equal to 5^17×4^9? GMAT Problem Solving
• In a Shooting Competition, Probability of A Hitting Target is 2/5, by B is 2/3 and C is 3/5 GMAT Problem Solving
• The Sides of a Quadrilateral Taken in Order are 16,16,14 and 10 GMAT Problem Solving
• If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days GMAT Problem Solving
• If denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> GMAT Problem Solving
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
• What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving