Math Word Problems & Logic Puzzles

The mean of two consecutive primes is (p1 + p2)/2. For all primes greater than 2, primes are odd, so their sum is even and the mean is an integer. However, that integer always lies between the two primes; since there are no primes between consecutive primes, the mean cannot be prime.

If Banu spent 85% of her money, she has 15% remaining. If 15% equals Rs. 75, then 100% equals Rs. 75 × (100/15) = Rs. 500. Check: 85% of 500 = 425, leaving 500 - 425 = 75. ✓

Each year, the car retains 75% (100% - 25%) of its value. After 5 years: Value = 16000 × (0.75)^5 = 16000 × 0.2373 ≈ 3796.88. This compounds the depreciation annually.

The series lists polygons in order of increasing sides: Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6). The next is Heptagon (7 sides). Note: 'Petagon' is a typo for Pentagon.

Percentage = (23/27) × 100 = 85.185%. Rounding to the nearest percent gives 85%. Option C is correct. The distractor 91% comes from (23/25), and 82% from roughly 23/28.

For a 5-year average of 20 books, total books = 20 × 5 = 100. Sum of first 4 years = 23 + 17 + 20 + 19 = 79. Year 5 = 100 - 79 = 21. This maintains the average.

Let the number be x. Condition: x + 1/x = 2x. Solving: 1/x = x, so x^2 = 1, giving x = 1 (natural number). Check: 1 + 1/1 = 2, which equals 2 × 1 = 2. ✓ Option B is correct.

Let Pradeep's age be x. Sandeep is x+2 years old. Their sum is x + (x+2) = 106, which gives 2x = 104, so x = 52. Option D is correct. Option C (45) would make Sandeep 47, summing to only 92. Option B (53) would make Sandeep 55, summing to 108.

The scale is 3 inches to 5 feet, meaning every inch on the blueprint represents 5/3 feet in reality. For 9 inches on the blueprint: 9 × (5/3) = 15 feet. Option B is correct. Option A (25 ft) incorrectly uses 9:5 as the ratio directly.

Let c = chickens and p = pigs. Heads: c + p = 200. Legs: 2c + 4p = 540. Substituting c = 200-p into the legs equation: 2(200-p) + 4p = 540, giving p = 70 pigs. Then c = 200 - 70 = 130 chickens. Option D is correct. Option A (70) gives the number of pigs, not chickens.

Let son's age 3 years ago be s. Then father was s+24. Currently: son = s+3, father = s+24+3 = s+27. Given father = 5 × son: s+27 = 5(s+3). Solving: 4s = 12, so s = 3. Son's current age = 6, and three years from now he'll be 9. Option D is correct.

Two linear equations have no unique solution when the lines are parallel or coincident, meaning the ratio of x and y coefficients is equal. For no unique solution: 3/4 = k/12, giving k = 9. Option B is correct. When k = 9, the second equation becomes 9x + 12y = 30, or 3x + 4y = 10, which is parallel to the first equation 3x + 4y = 12.

Let fare = F and reservation = R. F + R = 216. Adult + Child = (F + R) + (0.5F + R) = 327. Substituting 216: 216 + 0.5F + R = 327 => 0.5F + R = 111. Subtracting this from F + R = 216 gives 0.5F = 105, so F = 210.

Let the original sum of 30 friends' weights be S. The new average after adding the coach is 31 kg for 31 people, so total weight = 31 × 31 = 961 kg. The average increased by 1 kg, so original average was 30 kg, giving S = 30 × 30 = 900 kg. Coach's weight = 961 - 900 = 61 kg. Option B is correct. Option C (60) ignores that the coach raises the average by 1 kg for 31 people.

The question relates the name of the shape to a number. A circle is often associated with 1 (one continuous line), and an octagon is defined by having 8 sides and 8 angles, making 8 the logical answer.

Each man forms a right triangle with legs of 4m and 3m. The hypotenuse (distance from start) for each is 5m (sqrt(4^2 + 3^2)). Since they walked in opposite directions, they are 5m + 5m = 10m apart.

The relationship is based on categories: Pear and Apple are both fruits. Therefore, Potato must be paired with another vegetable. Radish is a root vegetable like a potato. Banana, strawberry, and peach are fruits, and lettuce is a leaf vegetable.

Ten thousand is 10,000; one hundred is 100; and twelve is 12. Summing these gives 10,112. 10120 represents ten thousand one hundred and twenty, and 11012 represents eleven thousand and twelve.