Math and Puzzles Quiz

Using the numerals 1, 7, 7, 7, 7 to create 100: 177 - 77 = 100. This uses all five required digits exactly once. Other options like 177/77 ≈ 2.3, 717/77 ≈ 9.3, and 771/77 ≈ 10.0 are incorrect.

Let the 5-digit number be N. If we put 1 at the end, we get 10N + 1. If we put 1 at the beginning, we get 100000 + N. The condition says 100000 + N = 3(10N + 1), which simplifies to 100000 + N = 30N + 3, giving 99997 = 29N, so N = 42857.

A parallelogram has four sides, but the angles are not necessarily congruent. Only in a rectangle (a special type of parallelogram) are all angles equal to 90 degrees. In a general parallelogram, opposite angles are equal, but adjacent angles are supplementary, not congruent. Therefore, the statement is false.

An isosceles triangle has at least two equal angles (and consequently two equal sides). This triangle has angles 110°, 30°, and 40° - all three are different, making it a scalene triangle, not isosceles.

A rhombus is a quadrilateral with all sides equal, but angles need not be 90°. A square is a special type of rhombus with right angles. Therefore, while all squares are rhombuses, not all rhombuses are squares.

An oblique angle is any angle that is not a multiple of 90° (not 0°, 90°, 180°, 270°, etc.). Angles greater than 180° are called reflex angles, not oblique angles. The statement incorrectly identifies the term.

Using the triangle area formula Area = (1/2) × base × height, we can solve for base: base = (2 × Area) ÷ height. With Area = 36 cm² and height = 4 cm, base = (2 × 36) ÷ 4 = 72 ÷ 4 = 18 cm, not 16 cm as stated.

This is a classic trick question - if you take 2 apples away, you possess those 2 apples. The answer tests reading comprehension rather than arithmetic skills, as many incorrectly calculate 3-2=1.

The three pills span 60 minutes total: take the first at 0 minutes, the second at 30 minutes, and the third at 60 minutes. This is a timing puzzle - the duration is from the first to the last pill, not the cumulative interval.

Every month of the year has at least 28 days - February has 28 or 29 days, while the other months have 30 or 31. The trick is recognizing that 'having 28 days' doesn't mean 'having only 28 days' - all months satisfy this condition.

The phrase 'all but 9 die' means that 9 sheep survive - they are the exception that didn't die. This tests language comprehension rather than arithmetic, as many mistakenly calculate 17-9=8.

A dead man cannot legally marry anyone - marriage requires two living people. The statement creates a logical contradiction because if the man has a widow, he is deceased.

Given 2x - y = 4. To find 6x - 3y, notice that 6x - 3y = 3(2x - y). Substituting the given value: 3(4) = 12. This is a direct application of multiplying both sides of an equation by a constant.

Combined rate = 1/20 + 1/30 - 1/40 = 6/120 + 4/120 - 3/120 = 7/120 tank per minute. Time = 120/7 = 17 1/7 minutes. This is a standard work rate problem with one outlet.

Assuming the notation means (1/10)^18 - (1/10)^20: Factor out (1/10)^18 to get (1/10)^18[1 - (1/10)^2] = (1/10)^18[1 - 1/100] = (1/10)^18(99/100) = 99/10^20 = 99/1020. This uses exponent factoring.