⚖️ Three friends, weighed two at a time

A closer look at one question · SMC 2026 mock, Question 15 (bank id A15)

Jim and two friends weighed themselves in pairs. John is the LIGHTEST and Jack is the HEAVIEST. The three readings were 56 kg, 70 kg and 54 kg (in no particular order). Find Jim's weight.

1 Sort the readings first — smallest to largest

readingsorted
54, 56, 7054 (smallest) → 56 → 70 (biggest)

The SMALLEST pair must be the two lightest people: John + Jim = 54. The BIGGEST pair must be the two heaviest: Jim + Jack = 70. What is left over, John + Jack = 56.

2 Add all three readings — everyone is counted TWICE

Sum
54 + 56 + 70 = 180
÷ 2
John + Jim + Jack = 90

3 Take off the ONE pair with no Jim in it

"John + Jack" (56) is the pair that leaves Jim out, so:

Jim
90 − 56
34 kg

The trap: assuming the readings are listed in a helpful order (that the 1st reading is John + Jim). Sort them smallest to largest first — it is the smallest and largest pairs that the clue actually pins down.