This means this is a “1 – probability()” question…this is the default strategy when a question is asking the probability of at least X happening. It translates into 1 – probability(that event NOT happening)

Step 2:
Now you need to find the probability of not getting a pair for each of the 4 cards. Recognize that as you go through each card, the number of available cards from the remaining deck is constantly changing. Originally you have 12 cards, but then after you put down 1 card, u have 11 cards left.

Step 3:
1st card = any card = prob of 1 or 100%
2nd card = any card except the value of first card = 10 out of 11 choices
3rd card = any card except first card and except second card = 8 out of 10 choices
(notice we must exclude the 1st card and the 2nd card–but also the corresponding pairs for each of these cards.
4th card = any card except first/second/third card (and their corresponding pair card) = 6 out of 9 choices

Now multiply these probabilities so you know what the probability of NOT getting any pairs for all 4 iterations.
10/11 * 8/10* 6/9 = 480 / 990

1 – 480/990 = 510/990 = 17/33

Answer choice is C (17/33)

I don’t recommend using the nCr formula here, but if you want to use nCr’s, then:

= 1 – prob(choosing all different cards
= 1 – prob(choosing 4 different cards out of 6) * (possibilities for first card to be of two suits, for second card to be of two suits, for third card to be of two suits, and for fourth card to be of two suits)
= 1 – (6c4 * 2 * 2 * 2 * 2) / (12c4)
= 1 – (15 * 16) / (( 12 * 11 * 10 * 9 )/(4*3*2*1))
= 1 – 240 / 495
= 255/495

= 51/ 99
= 17 / 33

But again, this is not the most efficient way to think through this question. The best way is to count according to the method I discussed first above.
_________________
———————
Zeke Lee
Co-Founder, The GMATPill Study Method
http://www.gmatpill.com
98%ile GMAT in 2 weeks

The answer here is A. Let me explain.

The structure of the sentence is: Aerugo is [X], and is [Y].
where x = “the green bloom visible on many copper items”
y = “produced over the course of time”

Don’t confuse this with the sentence structure that most people would see initially:
Aerugo is the green “bloom” [X], and [Y]
where x = visible on many copper items
y = is produed

At first glance, there may seem like something is wrong with A just because of the way they underline the sentence.
But if you step back and look at what the real structure of the sentence is, you’ll notice the keyword AND. Look to the left and look to the right.

On the left you should see “is the green bloom visible on many copper items” and on the right you should see “is produced over the course of time.”

This is consistent.

All choices (B), (C), and (D) are incorrect because the end of the answer choices use the active verb “Produces” or “that produces” or “which produces”—you need to ask yourself: “Produce what?”
Well, if you sub it into the sentence, you’ll see: “that produces, like iron rust, over the course of time”
That doesn’t make sense! You don’t just “produce over the course of time.” You need to produce something. You need to produce [x].
Since it doesn’t make sense, all of them (B, C, and D) don’t make sense.

Now, (A) does work because it does not follow this structure. Rather, it says the Aerugo “is produced, like iron rust, over the course of time.” This makes sense. Combine that with our analysis above with the X & Y consistency and you’ll see that answer (A) is correct.

Hope this helps!

I surprisingly got to the answer D within 30 seconds. Let me show you how.

Step 1) Identify multiple commas—this is not a “laundry list” but rather several descriptive phrases. “Ultrathin” and “layered” are just words that describe “CONSTRUCTION.”

Step 2) The phrase “the same as the one making some butterflies shimmer” actually describes the “CONSTRUCTION of a butterfly’s wings“—NOT “wings” by itself.

Step 3) Cut the fluff:
“Scientists have recently discovered that the ultrathin, layered construction of a butterfly’s wings, the same as the one making some butterflies shimmer via the phenomenon of iridescence, are enabling the insect to control how much heat energy is absorbed by its wings and how much is reflected away. ”

Construction are enabling? Doesn’t make sense! So you know (A) is wrong.

It should be:

“Scientists have recently discovered that the ultrathin, layered construction of a butterfly’s wings, the same as the one making some butterflies shimmer via the phenomenon of iridescence, enables the insect to control how much heat energy is absorbed by its wings and how much is reflected away. ”

Step 4) Browse through the answer choices–but don’t read them from the beginning—look at the last few words: that also enables, enabling, also enables, also enable…

Which ones make sense? The “construction” of these guys (where “construction” is singular) ENABLES.
You must use “ENABLES”—so either (B) or (D).

Step 5) Note (B) has the extra word “that”—unnecessary. Also, it uses the word “which”—this implies the phrase describes “wings” when structurally the phrase really describes the “construction of the wings”–not the “wings.”

Therefore, (D) is the answer.

If you know how to strategically approach questions like these, you can most efficiently answer them in as little time as possible.

A student sent me a question regarding something he came across in a GMAT Workbook. He/she came across a past/present/future verb framework issue that made him puzzled and cost him time to answer the correct question. Take a look, hope you don’t make the same mistake.

Employing groundbreaking techniques in alternative medicines, the patient’s health improved in a few days.
Employing groundbreaking techniques in alternative medicines, the doctors saw the patient’s health improve in a few days.

I think this answer is incorrect. Improve should be Improved.
Please explain.