SAT Math Question. (Trial and error)

Test Preparation SAT Preparation
1

<p>Each time Shannon pushes the button on a machine, a bell rings 7 times. Each time she turns the switch on the machine, the bell rings 3 times. During one hour, Shannon caused the bell on the machine to ring 23 times. How many times did she push the button?
The answer is 2.</p>

<p>However, I don’t know how to get that. I tried 23/7 remainder = 3… But since the answer is 2 and not anything more, I don’t know how to proceed any further.</p>

<p>Could anyone please work this out and explain it?
Thank you. :)</p>

2

<p>Since the bell rang 23 times. You can divide 23 by 7. And that will be 3 remainder 2, but since you cannot get the last 2 rings since 3 is not divisible by 2 into integral values. You can try 2 pushes of the button which gives 14 rings. 23-14 = 9, and 9 is divisible by 3. Therefore 2 is the answer.</p>

3

<p>Makes perfect sense! (I was confusing the switch with the button. :p)</p>

<p>Thank you pokrat! :)</p>