My Pals Are Here Maths Pdf 5a [WORKING]

Number of terms: ( 180 \div 18 = 10 ) multiples of 9 with even multipliers (2,4,6,…,20) → yes, 10 terms.

She called two students, Lin and Ravi, from the My Pals Are Here Maths 5A class for help.

[ \text{Total} = \frac{n \times (n + 1)}{2} = \frac{180 \times 181}{2} = 90 \times 181 = 16,290 ] Stack A = 6, 18, 30, …, 180. This is an arithmetic sequence: first term 6, last term 180, common difference 12. My Pals Are Here Maths Pdf 5a

Sum of Stack A = (\frac{15}{2} \times (6 + 180) = 7.5 \times 186 = 1,395). Stack B = 18, 36, 54, …, 180. First term 18, last term 180, common difference 18.

Better: A: 6×(odd) = 18k? Let odd=2m+1. Then 6(2m+1)=12m+6. For this to be multiple of 18: 12m+6 divisible by 18 → 12m+6=18p → divide 6: 2m+1=3p → 2m+1 odd multiple of 3. B: 9×(even)=9×2n=18n. So A∩B = numbers that are 18×k where k is both an odd integer (from A) and any integer (from B) → Wait B's even multiplier: 9×2n=18n, so B includes all multiples of 18. A's odd multiplier: 6×(odd) = 6,18,30,42,54,66,78,90,102,114,126,138,150,162,174. Multiples of 18 in that list: 18,54,90,126,162 → yes 5 numbers. Those are in A∩B. So intersection size = 5. Number of terms: ( 180 \div 18 =

Sum of intersection: 18+54+90+126+162 = (18+162)=180, (54+126)=180, plus 90 → 180+180+90=450. Stack C = Total − (Sum A + Sum B − Intersection) = 16,290 − (1,395 + 990 − 450) = 16,290 − (2,385 − 450) = 16,290 − 1,935 = 14,355 . Step 7: The twist Lin announced, "Miss Lee, Stack C's total is 14,355."

Ravi added, "And now we can reassemble the exam papers correctly." This is an arithmetic sequence: first term 6,

Number of terms: ( 180 \div 6 = 30 ) multiples of 6, but only odd multipliers → half of them? Let’s check: Multiples of 6 up to 180 = 6×1 to 6×30 (30 numbers). Odd multipliers: 1,3,5,…,29 → that’s 15 terms.