I chose C mistaking that Stat1 is absolute. If Stat1 did not say "No more than", then would I be able to say that 1+2 is sufficient?
I'm happy to respond.
Because we are dealing with people, it would be impossible for both percents to equal 90% and for the number of managers not coming to equal only 7. You see, when the prompt says, "ninety percent of the expected number of managers attended a conference
," that's not 90%, rounded to the nearest whole number. It actually means exactly, mathematically, 90%. In other words, the number of expected managers must be divisible by 10, and 9/10 of them came to the conference, and 1/10 didn't. It also must be true that
(1/10)* (expected number) + (those not expected) = 7
For example, consistent with this statement:
16 managers, ten expected to go, 9 of the expected went, and 7 didn't attend. Expected/whole = 10/16 = 5/8 = .625, lower than 90%
25 managers, 20 expected to go, 18 of the expected went, and 7 didn't attend. Expected/whole = 20/25 = 0.8, lower than 90%
34 managers, 30 expected to go, 27 of the expected went, and 7 didn't attend. Expected/whole = 30/34 ---
Is 30/34 less than 90%? Well, 1/10 of 34 is 3.4, and 30 is less than (34 - 3.4), so it's below 90%.
43 managers, 40 expected to go, 36 of the expected went, and 7 didn't attend. Expected/whole = 40/43 ---
Is 40/43 less than 90%? Well, 1/10 of 43 is 4.3, and 40 is more than (43 - 4.3), so it's more than 90%.
You see, none of these had the percent of expected/whole equal precisely 90%. In order for both percents to equal precisely 90%, the total number of managers would have to be a multiple of 100. Say:
Total managers = 100
Percent expected to do = 90
Percent of the expected who went = 81
Number who didn't go = 100 - 81 = 19
Any multiple of this scenario would require that the number who didn't go be a multiple of 19. That's inconsistent with this scenario, which is why both percents can equal precisely 90 at the same time.
Does this make sense?
Magoosh Test Prep