If an anglet is defined as 1 percent of 1 degree then how ma

Question

If an anglet is defined as 1 percent of 1 degree then how many anglets are there in a circle

A. 0.36
B. 3.6
C. 360
D. 3600
E. 36000

mikemcgarry · Answer

Hi, there! I'm happy to help with this.

First of all, it's important to appreciate: this is one of those questions where the GMAT makes up a brand new term, defines it on the spot, and during the questions on the test is the first time that any test-taker has seen it. Outside of this question on the GMAT, no one has ever heard of an anglet. So, first of all, don't worry! This is not something your geometry teacher explained in detail while you weren't paying attention.

Whenever the GMAT does this -- introduces a brand new term or symbol --- they have to tell us, right there and then, exactly what is meant by it. Here, they tell us: an anglet is defined as 1 percent of 1 degree. Think about what that means. Think about what a percent is. A percent, by definition, is a fraction out of 100. For example, 47% is 47/100. This means that 1% is 1/100 --- when you have 1% of something, you have one-part-in-a-hundred of it. If 1 anglet = 1% of a degree, then multiply by 100 --> 100 anglets = 100% of a degree, or in other words, 100 anglets = 1 degree. That's where the idea of 100 anglets in a degree comes from --- again, it's not something you were suppose to know from outside this question; rather, it was something you were suppose to figure out from the properties of percents. 1 degree = 100 anglets, so in a full circle, 360 degrees = 36000 anglets, Answer E. Here's another percents question, just for additional practice. https://gmat.magoosh.com/questions/952 That link should include both the question and a video explanation of the answer. Does my explanation make sense? Please let me know if you have any further questions about this. Mike

morya003 · Answer

Hi Mike
Thanks very much - that was silly of me.
I came across this question in the 12th OG and I am very worried if the approach given in OG is correct - we will have to unlearn everythng that we have learnt and leave our scores to chance !!
The OG question and solution is given below and honestly I think the solution is wrong - the intersection has to be subtracted and not added !!
Please advise - straightforward formula for this is 
set A + set B + neither - both = total
60 + 3x + 80 - x = 200
x = 30
Please help.

Original question and solution
A marketing firm determined that, of 200 households
surveyed, 80 used neither Brand A nor Brand B soap,
60 used only Brand A soap, and for every household
that used both brands of soap, 3 used only Brand B
soap. How many of the 200 households surveyed used
both brands of soap?
(A) 15
(B) 20
(C) 30
(D) 40
(E) 45
Arithmetic Operations on rational numbers
Since it is given that 80 households use neither
Brand A nor Brand B, then 200 – 80 = 120 must
use Brand A, Brand B, or both. It is also given
that 60 households use only Brand A and that
three times as many households use Brand B
exclusively as use both brands. If x is the number
of households that use both Brand A and
Brand B, then 3x use Brand B alone. A Venn
diagram can be helpful for visualizing the logic

All the sections in the circles can be added up
and set equal to 120, and then the equation can
be solved for x:
60 + x + 3x = 120
60 + 4x = 120 combine like terms
4x = 60 subtract 60 from both sides
x = 15 divide both sides by 4

Thank you in advance.
BR

mikemcgarry · Answer

BR

With the Set A and Set B stuff, we have to be very careful about wording.

If we add (Set A only) and (Set B only) with the (neither) group, then the group (both A & B) hasn't been counted at all, because those folks are not included in (Set A only) or (Set B only). Therefore, in that case, we have to add all four:

Total = (Set A only) + (Set B only) + (neither) + (both A & B)

If you think about it, those are the four separate regions on an standard Venn Diagram.

It's very different if we add (everyone in A) and (everyone in B), because each one of those sets includes the people in (both A & B). When we add those first two, the group (both A & B) gets counted twice, and we have to subtract the overlap.

Total = (everyone in A) + (everyone in B) + (neither) - (both A & B)

You see, you were simply writing (Set A) + (Set B), without making the distinction of (Set A only) vs. (everyone in Set A).

The OG solution is correct, because they had specified (Set A only) and (Set B only) and solved accordingly, but you were interpreting those as (everyone in Set A) and (everyone in Set B). Does that make sense?

Please let me know if you have any more questions.

Mike

morya003 · Answer

Hi Mike 
Thanks ...but am still not entirely sure...because even in the OG they give 2 circles

1st circle 60
2nd circle 3x
intersection x

if you add all the above 3 as per OG then you are counting brand A and B twice

If you want to add then they should be added as follows

(60-x)+x+(3x-x)=120
60 + 2x = 120
2x = 60
x = 30

mikemcgarry · Answer

BR

I'm at home right now, and I don't have the OG with me, but according to your first post, the original text was:

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

Again, the crucial part is the wording. The 60 does not represent everyone who uses Brand A; it represents the folks who use "only Brand A." By definition, that excludes and does not count the people who use both Brand A and Brand B.

The question would be very very different if they said: "60 people use Brand A." That would imply that 60 is the number of everyone who uses Brand A, both the folks who use only Brand A and the folks who use both Brand A and Brand B. Often, on the GMAT, these set questions are set up that way, and when they give a number, it's a number that includes the "only" people and the "both" people.

Here, because of the precise wording, we know it's a different kind of question -- the 60 is "only Brand A", and include no overlap, no part of the "both" people.

Similarly, the 3x that we use for Brand B is technically for the folks who use "only Brand B" --- again, that contains no overlap and does not include any of the folks who use "both".

With the GMAT, you can rely on the wording to give you all the precision you need. I don't have the OG with me, so I can't see the diagram to which you are referring, but based on the wording of the question, I am going to say about that diagram:

= The 60 refers not to the whole circle but to the "lune" --- or whatever you want to call the piece of the circle left when you subtract the overlap. I attached a rough diagram to demonstrate this visually -- 60 is not the circle, but rather the lune.
= Similarly, the 3x refers not to the other circle, but again, to the "lune" on that side.
= x is the overlap, the part included in neither "lune"

Therefore, when you add 60 + x + 3x, there's absolute no overlap to be subtracted, because those are three mutually exclusive and non-overlapping conditions.

We know they are mutually exclusive and non-overlapping because the question text was precise in specifying "only Brand A" and "only Brand B."

Does this clear things up? Please let me know if you have any further questions.

Mike

Attachments

the Venn lune.jpg [ 134.52 KiB | Viewed 7878 times ]

PareshGmat · Answer

1% of degree = 1/100
So 1 anglet = 1/100 Degree
So, how many anglets =   360/(1/100)... solving the same = 36000

Srikantchamarthi · Answer

PareshGmat  hi,

can you please explain the fraction part?

Thanks

u1983 · Answer

1% of 1 degree is 1 anglet
hence, 1 degree or 100% of 1 degree is 100 anglet.
Thus full-circle or 360 degree is 100*360 =36000 anglet ............  Ans e

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If an anglet is defined as 1 percent of 1 degree then how ma

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