math & puzzles Online Quiz - 127

Calculate area to price ratio: 10" pizza area = π×5² = 25π sq in, price = $3.99, so $3.99/25π = $0.0508 per sq in. 14" pizza area = π×7² = 49π sq in. At same ratio: 49π×$0.0508 = $7.82. Actual price $7.04 is $0.78 less. Discount = 0.78/7.82 = 0.0997 ≈ 10%. Alternative method: area increases by factor 49/25 = 1.96. Price should increase to $3.99×1.96 = $7.82. Actual is $7.04, so discount = (7.82-7.04)/7.82 ≈ 10%.

The sequence A, M, J, J, A, S represents the first letters of months: April (4th month), May (5th), June (6th), July (7th), August (8th), September (9th). The next month is October, so the answer is O.

Build the chain: Lucy > Kyle > Trevor (Kyle older than Trevor) and Lucy > Sam > Kyle. Lucy is older than both Sam and Kyle, and Trevor is younger than Kyle who is younger than Lucy. This makes Lucy the eldest.

Build the chain: Ed > Jasmin > Harold > Bea. The order is Ed (eldest), then Jasmin (second eldest), then Harold, then Bea (youngest). Jasmin is indeed the second eldest.

Build the chain: Tina > Mike > Riley > Malcolm. The order is Tina (eldest), Mike, Riley (second youngest), Malcolm (youngest). Riley is the second youngest, not the youngest.

Build the chain: Rebecca > Liam > Nina > Josh. The order is Rebecca (eldest), Liam (second eldest), Nina (third), Josh (youngest). Liam is indeed the second eldest.

Build the chain: Monica > Cindy > Brooke > Mandy. The order is Monica (eldest), Cindy, Brooke, Mandy (youngest). Mandy is indeed the youngest.

Build the chain: Harold > Jake > Paul > Nick > Max. The order is Harold (eldest), Jake, Paul, Nick, Max (youngest). Max is indeed the youngest. The options don't include Max's label clearly, but E is Max.

Build the chain: Tegan > Leanne > Kirstie > Bonnie > Casey. The order is Tegan (eldest), Leanne (second eldest), Kirstie, Bonnie, Casey (youngest). Leanne is the second eldest.

Build the chain: Ashlee > Angela > Katerina > Aleisha > Gabrielle. The order is Ashlee (eldest), Angela, Katerina, Aleisha (second youngest), Gabrielle (youngest). Aleisha is the second youngest.

Build the chain: John > Marion > Linda > Peter > Sarah. The order is John (eldest), Marion, Linda, Peter, Sarah (youngest). John is indeed the eldest.

Build the chain: Keith > Ruth > Emerald > Donald. The order is Keith (eldest), Ruth, Emerald (second youngest), Donald (youngest). Emerald is the second youngest.

The unit digit of powers of 3 cycles in a pattern: 3, 9, 7, 1. Since 1244 is divisible by 4 (1244/4 = 311 with remainder 0), 3^1244 has the same unit digit as 3^4, which is 1.

When a number is divided by 36 and leaves remainder 19, we can write: Number = 36k + 19 for some integer k. Since 36 = 12 × 3, when we divide by 12, we get: Number = 12(3k) + 12 + 7 = 12(3k+1) + 7. Thus the remainder is 7. Option C (192) is incorrect as it's greater than the divisor 12.

Let total days = d. A works for (d-10) days at rate 1/20 per day. B works for d days at rate 1/30 per day. Equation: (d-10)/20 + d/30 = 1. Solving: (3(d-10) + 2d)/60 = 1 → 5d-30 = 60 → 5d = 90 → d = 18. Check: A works 8 days (8/20 = 0.4), B works 18 days (18/30 = 0.6), total = 1 job.

Let original average = x kg for 60 students. Total weight = 60x. When 45 kg student leaves, remaining 59 students have average (x + 0.2) kg. Their total = 59(x+0.2) = 59x + 11.8. Also, 59x + 11.8 = 60x - 45 (subtracting the student who left). Thus: 11.8 + 45 = x → x = 56.8. New average = 56.8 + 0.2 = 57 kg.

Let apple cost = a, mango cost = m. Equation 1: 5a + 4m = 36 × 9 = 324. Equation 2: 7a + 8m = 48 × 15 = 720. Subtract 2×Eq1 from Eq2: (7a+8m) - (10a+8m) = 720 - 648 → -3a = 72 → a = 24. Then 5(24) + 4m = 324 → 120 + 4m = 324 → 4m = 204 → m = 51. Cost of 24a + 24m = 24(24+51) = 24 × 75 = 1800. Wait - let me recalculate: From 5a+4m=324, if a=24, then 120+4m=324, m=51. Then 24a+24m = 24(24)+24(51) = 576+1224 = 1800. But answer is 2088. Let me verify: Actually 24 apples + 24 mangoes = 24 × (a+m) = 24 × (24+51) = 24 × 75 = 1800. Hmm. Let me check the equations again: 5a+4m=324 (correct). 7a+8m=720 (correct). Multiply first by 2: 10a+8m=648. Subtract from second: (7a+8m)-(10a+8m)=720-648 → -3a=72 → a=-24? That can't be right. Let me redo: 7a+8m=720 minus (10a+8m=648) gives -3a=72, so a=-24. That's negative, which is impossible for prices. Let me recalculate the averages: Average of 5 apples + 4 mangoes (9 items) = 36, so total = 36×9 = 324 ✓. Average of 7 apples + 8 mangoes (15 items) = 48, so total = 48×15 = 720 ✓. From first equation: 5a + 4m = 324. From second: 7a + 8m = 720. Multiply first by 2: 10a + 8m = 648. Now subtract from second: (7a+8m) - (10a+8m) = 720 - 648. This gives -3a = 72, so a = -24. This is mathematically correct but gives negative price, which suggests the claimed answer may be wrong, OR I'm misunderstanding. Let me try a different approach: From 5a+4m=324 and 7a+8m=720. From first: 4m = 324-5a, so m = (324-5a)/4. Substitute: 7a + 8(324-5a)/4 = 720 → 7a + 2(324-5a) = 720 → 7a + 648 - 10a = 720 → -3a = 72 → a = -24. Then m = (324-5(-24))/4 = (324+120)/4 = 444/4 = 111. So a = -24, m = 111. Then 24a + 24m = 24(-24+111) = 24(87) = 2088. So mathematically, the answer is 2088, even though apple price is negative. The claimed answer (B: 2088) is mathematically correct based on the given equations.

Let original price = P, quantity = Q. New price = 1.25P. New spend = 1.15PQ (15% more). New quantity = (1.15PQ)/(1.25P) = 0.92Q. So quantity reduces by 8%. Formula: (1+%spend)/(1+%price) - 1 gives the % change in quantity. (1.15/1.25) - 1 = 0.92 - 1 = -0.08 = -8%.

Given A:B = 3:2 and B:C = 3:2. Let B = 6x (LCM of 2 and 3). Then A = 9x (since A/B = 3/2) and C = 4x (since B/C = 3/2 → C = 2B/3 = 4x). Total runs = 9x + 6x + 4x = 19x = 342. So x = 18. Therefore A's runs = 9x = 9 × 18 = 162. Check: B = 108, C = 72, total = 162+108+72 = 342 ✓.

P(at least one hit in 4 shots) = 1 - P(no hits) = 1 - (3/4)^4 = 1 - 81/256 = 175/256. Each shot is independent with P(hit) = 1/4.