Query about question "$A$ and $B$ play a guessing game..." [22]

[user11104]

https://www.gregmat.com/problems/quant?problem=a-and-b-play-a-guessing-game

I’m trying to solve this question using backsolving rather than algebra. My approach is to reverse the operations: add 5, divide by 6, subtract 3, and multiply by 2.

I understand why 9001 works: 9001+5=9006, which is divisible by 6, giving an integer starting value.

However, I’m confused about the last option, 9004. When I backsolve, I get 9004+5=9009, and 9009/6=1501.5, so I eliminate it. Is this the correct way to eliminate 9004?

Could someone explain the backsolving approach step-by-step, particularly why 9004 does not work?

[Kweku]

@user11104

However, I’m confused about the last option, 9004. When I backsolve, I get 9004+5=9009, and 9009/6=1501.5, so I eliminate it. Is this the correct way to eliminate 9004?

The final answer must be an integer, not an answer you get mid-operation.

@user11104

Could someone explain the backsolving approach step-by-step, particularly why 9004 does not work?

• 9004 + 5 = 9009

• \frac{\text{9009}}{\text{6}} = 1501.5

• 1501.5 - 3 = 1498.5

• 1498.5 × 2 = 2997

Again, the final answer is what’s supposed to be the integer after doing all operations.