Finding of a survey of Systems magazine subscribers
Finding of a survey of Systems magazine subscribers: Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year were placed by subscribers under age thirty-five.
Finding of a survey of advertisers in Systems magazine: Most of the merchandise orders placed in response to advertisements in Systems last year were placed by people under age thirty-five.
For both of the findings to be accurate, which of the following must be true?
(A)
(B)
(C)
(D)
(E)
The complete question cannot be pasted here because of copyrights.
The first statement says:
Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year were placed by subscribers under age thirty-five.
Many people find this statement hard to understand, partly because they try to assimilate the whole statement in one go. I don’t do so. I assimilate the statement part by part. For example, the way I’m going to assimilate this statement is as below
Thirty percent of all merchandise orders
I read the above part, and I understand that it’s talking about 30% of all merchandise orders. The set of orders is “All merchandise orders”.
Then, I read the next part.
Thirty percent of all merchandise orders placed by subscribers
Thirty percent of all merchandise orders placed by subscribers in response to advertisements
Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine
Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year
The modifier “last year” creates a subset of the above set. Now, we’re not talking about “all merchandise orders placed by subscribers in response to advertisements in the magazine”; we’re talking about merchandise orders placed by subscribers in response to advertisements in the magazine last year, which is a subset of “all merchandise orders placed by subscribers in response to advertisements in the magazine”.
The other subset is “all merchandise orders placed by subscribers placed in response to advertisements in the magazine in years other than last year”.
After “last year”, we have a verb “were placed” in the sentence. This means that the definition of the set is complete.
So, which set does the sentence talk about?
All merchandise orders placed by subscribers placed in response to advertisements in the magazine last year (The orange circle above)
Given the way I’ve presented above, it may seem to you that the set we’re talking about is a very small subset of “All merchandise orders”. This need not be true. We just know that it’s a subset of “All merchandise orders”. How small? We don’t know. For example, the image on the right-hand side is also possible.
It is possible for our subset to be even equal to the set of “All merchandise orders”.
When would it be the case? Think about it.
- If no non-subscriber placed the orders, the set of “All merchandise orders placed by subscribers” would be equal to the set of “All merchandise orders”
- If there we no subscribers who placed the orders that were placed not in response to advertisements (i.e. every subscriber who placed the orders placed the orders in response to advertisements), the set of “All merchandise orders placed by subscribers in response to advertisements” would be equal to the set of “All merchandise orders placed by subscribers”.
- If there we no subscribers who placed the orders in response to advertisements OUTSIDE the magazine (e.g. advertisements on TV), the set of “All merchandise orders placed by subscribers in response to advertisements in the magazine” would be equal to the set of “All merchandise orders placed by subscribers in response to advertisements”.
- If there we no subscribers who placed the orders in response to advertisements in the magazine in years other than last year (e.g. orders placed two years ago in response to advertisements in the magazine), the set of “All merchandise orders placed by subscribers in response to advertisements in the magazine last year” would be equal to the set of “All merchandise orders placed by subscribers in response to advertisements in the magazine”.
- If all the above four conditions are satisfied, the orange circle (the set we’re talking about) will be equal to the black circle (the set of all merchandise orders)
Coming back to our original statement:
Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year were placed by subscribers under age thirty-five.
As I said, I read the above statement part by part to arrive at the understanding that this statement is talking about 30% of the orange set of orders. When I read the next part “were placed by”, the gist I have in mind is “30% of these orders”. So, I read the statement as:
Thirty percent of these orders were placed by subscribers under age thirty-five.
I see. The statement says that 30% of these specific orders were placed by subscribers under age thirty-five.
My question for you:
Who placed the remaining 70% of these orders?
Because the set of orders here is the set of orders placed by subscribers. As discussed above, the set corresponding to the red circle and all its subsets correspond to orders placed by subscribers. By definition of the set, the orders in these sets CANNOT be placed by non-subscribers.
For example, 30% of the orders placed by Indians were placed by Indians under the age of 35.
Who placed the remaining 70% of the orders?
Indians equal to or over the age of 35. Right? These orders cannot be placed by non-Indians. Why? Because the statement is talking about “orders placed by Indians”.
On the other hand, let’s look at the below statement:
30% of the orders were placed by Indians under the age of 35.
Here, who placed the remaining 70% of the orders?
Indians equal to or over the age of 35 OR Non-Indians. Here, non-Indians can place the orders we’re talking about since we are talking about “the orders”, not “the orders placed by Indians”. The verb part “were placed by Indians” doesn’t define the set. Only the modifiers of the noun depicting the set define the set by creating subsets.
The verb part NEVER defines the set. Only the modifier of the noun depicting the set defines the set by creating its subset.
Do you realize that in all of the above text, we’ve tried to understand just the first statement of the question?!
Try to read the second statement also part-by-part. The process remains the same.
Does the second statement talk about a set different from the set talked about in the first statement?
The answer is YES.
If you’re paying close attention you’ll observe that in the second statement, the definition of the set of orders doesn’t have the words “by subscribers”
First statement: Thirty percent of all merchandise orders placed by subscribers in response to advertisements in the magazine last year
Second statement: Most of the merchandise orders placed in response to advertisements in Systems
last year
If you’re wondering about the difference between “all merchandise orders” in the first statement and “the merchandise orders” in the second statement, don’t worry. There’s ZERO difference between the two. For example, the below two statements mean EXACTLY THE SAME.
- All orders placed by Indians were placed between 12 AM and 2 PM.
- The orders placed by Indians were placed between 12 AM and 2 PM.
Given that there’s one additional modifier in the definition of the set in the first statement compared to the set in the second statement, the first set is a SUBSET of the second set.
Let’s present the second set with a purple circle.
Our orange set is a subset of this purple set.
A question for you: In which scenario will this orange set be equal to the purple set?
In the scenario in which no non-subscribers placed orders in response to advertisements in the magazine last year. Please be aware that even in this scenario, non-subscribers could have placed orders, just that the orders were not placed in response to advertisements in the magazine last year.
We can depict the information presented in the two statements of the passage as below:
A question for you: given the information in the passage, can the orange circle be equal to the purple circle?
In other words, is it possible that no non-subscribers placed orders in response to advertisements in the magazine last year?
No. It’s not possible. If there were no non-subscribers who placed orders in response to advertisements in the magazine last year, the orange circle would be equal to the purple circle. In such a case, the two statements of the passage WILL CONTRADICT each other. If the orange circle is equal to the purple circle, the same statistic (30% or orders by people under age 35) should hold for the purple circle also. However, that is not so since the second statement mentions “most”, which means more than 50 percent.
Given that both statements are true, they cannot contradict each other. Thus, there have to be some non-subscribers who placed orders in response to advertisements in the magazine last year.
Let’s now look at the options:
(A) More subscribers to Systems who have never ordered merchandise in response to advertisements in the magazine are age thirty-five or over than are under age thirty-five.
Here also, I read the statement part by part. I’m not going to explain this statement part-by-part in the interest of space and time
The part “who have never ordered merchandise in response to advertisements in the magazine” is a modifier to “Subscribers to Systems”. Thus, we’re talking about specific subscribers to Systems. Which specific subscribers?
The ones who have never ordered merchandise in response to advertisements in the magazine.
What are we saying about these subscribers?
(A) More such subscribers to Systems are age thirty-five or over than are under age thirty-five.
We’re segmenting these subscribers into two age groups.
Thirty-five or over – More such subscribers
Under age thirty-five – Fewer such subscribers
In other words, we’re saying that a majority of such subscribers are age thirty-five or over.
However, given the two statements of the passage, do we know anything about the subscribers who have never ordered?
No. Thus, Option A is incorrect.
Let me create a variation of A by removing the word “never” from option A.
(A’) More subscribers to Systems who have ordered merchandise in response to advertisements in the magazine are age thirty-five or over than are under age thirty-five.
Is A’ correct?
No. Why? Let me ask you a question before I explain why A’ need not be true.
Which year is option A’ about? Is A’ about last year?
Some people say that A’ is about last year. They are wrong.
Some others say that A’ is about the current year. They are also wrong.
Let’s look at the following statement:
People who have killed a mosquito know how it feels to see blood in their hands.
Which people are we talking about in the above statement? People who killed a mosquito last year? People who killed a mosquito this year?
No. We’re talking about people who have killed a mosquito any time in the past. We’re talking about the entire past till the present moment. The verb tense in “have killed” is present perfect, which means the entire past till the present moment.
That is the same case with A’. A’ is talking about the entire past till the present moment. Do we have information beyond the last year in the passage?
No. So, A’ need not be true.
Now, let me create a variation of A’ by making it specific to last year.
(A’’) More subscribers to Systems who ordered merchandise in response to advertisements in the magazine last year are age thirty-five or over than are under age thirty-five.
Is A’’ correct?
No. Why?
Because the information in the passage is about orders, not subscribers.
While 30% of the orders were placed by subscribers under age 35, we cannot say that 30% of the subscribers were under age 35. It is entirely possible that a majority of the subscribers were under age 35 but that 70% of the orders were placed by subscribers equal to or over age 35.
(B) Among subscribers to Systems, the proportion who are under age thirty-five was considerably lower last year than it is now.
This option is wrong for the below two reasons:
- We cannot make a statement about the proportion of the subscribers in various age groups. The passage talks about orders, not subscribers.
- The passage nowhere talks about “now”. So, we don’t have any information about “now”.
(C) Most merchandise orders placed in response to advertisements in Systems last year were placed by Systems subscribers over age thirty-five.
Try to apply what you have learnt so far to this option. Which set of orders is this option about?
This option is about merchandise orders placed in response to advertisements in Systems last year i.e. the set that the second statement talks about – the purple circle.
If we look at the second statement of the passage, we know that most of such orders were placed by people under age 35. Given so, we have less than 50% orders left for people (subscribers and non-subscribers combined) equal to or over age 35. Given this, there is no way that subscribers over age 35 can place more than 50% of these orders. Thus, option C contradicts the information given in the passage.
Let’s talk about the negated version of option C.
(C’) Most merchandise orders placed in response to advertisements in Systems last year were NOT placed by Systems subscribers over age thirty-five.
Option C’ can be inferred from the given two statements, given the just discussed reasoning.
(D) Last year, the average dollar amount of merchandise orders placed was less for subscribers under age thirty-five than for those age thirty-five or over.
This option is quite easy to reject. The passage NEVER talks about the dollar amount; the passage is just about the orders. Thus, this option is incorrect.
(E) Last year many people who placed orders for merchandise in response to advertisements in Systems
were not subscribers to the magazine.
As we discussed during analysis of the two statements of the passage, there have to be some non-subscribers who placed orders for merchandise in response to advertisements in Systems last year. Given that there is a large difference in the two statistics (30% in the first statement and >50% in the second statement), it is reasonable to argue that there were many such non-subscribers last year.
Please understand that option E says “many”, not “most”. While “most” means more than 50%, “many” doesn’t have a clear mathematical equivalent. I can use “many” even for 3-4 persons.
You can find similarly detailed solutions on this link.