The Ultimate Q51 Guide [Expert Level]

This is a question related to the Common Mistake Type 4(A). You should be extra cautious on such type of questions.
If x, y are positive integers, what is the remainder when 2^(4x+2)+y is divided by 5?
1) x=3
2) y=1
Answer: B
Remainder questions that require you to divide the question by 5 has a cycle of 5. In other words, we get (~2)^1=~2, (~2)^2=~4, (~2)^3=~8, (~2)^4=~6.
Hence, the cycle of 4 is 24862486.
If we modify the original condition and the question, when we are dividing 2^(4x+2)+y by 5, we do not have to consider 4x. So, we need to consider only about 2^(2)+y. Since we only have to know y, the correct answer is B.

This is a type of questions that appears in the score range of 50-51.

This is one of the most challenging types of the question that looks like a journal. This is a PS question that you should be familiar with.

It is well-known that the way to find out approximation value of a positive integer n’s square root is following;
1st approximation: select a positive integer "a" and n is divided by a.
2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor.
What is the approximation positive integer n’s square root, in terms of a and n?
A. (a^2+n)/2a B. (a^2+n)/2 C. (a^2-n)/2a D. (a^2+n)/a E. (a^2+2n)/a
Answer: A
N=aQ, (a+Q)/2=(a+n/a)/2=(a^2+n)/2a

This type of questions looks very simple, but it is rather challenging. You should not underestimate the difficulty levels of PS questions (by the way this is a statistics problem).

As always, the more advanced questions combined with the mistake type 3 and 4 are frequently given on GMAT Math. Let's have a look at the question below, which is a current question. This question is also the mistake type 4(A), which is on the level of score 50-51. You have to be very confident with questions like this. You have to know the relation between approach method to variables and the mistake types. In particular, questions including number and ratio are frequently given, in which ratio is always an answer. The question below also contains 1) ratio and 2) number and the answer is A as well.

(ex 1) When x and y are integers, is x+y an even?
1) 3x+5y=even.
2) (x+1)2(y+1)2=even.

In the original condition, there are 2 variables. Hence, even though C could be the answer, considering the relationship between the Variable Approach Method and the Common Mistake Type, we can see that the condition 1) is always yes because x=y=even or x=y=odd. The condition is sufficient and the answer is A.

Answer: A

There is an increasing number of geometry questions. For example:
A quadrilateral is inscribed in a circle as above figure. What is the measurement of ∠R?
1) The radius of the circle is 5
2) The line segment PS is equal to the diameter of the circle.
Answer: B
The central angle is twice the angle of circumference. PRS=90 degrees. Hence, the correct answer is B.

(ex 2) A, B are two sets whose elements are integers, A∪B represent union set of two sets A, B. Is each of the elements in the set A divisible by 3?
1) A∪B={13,17,31,47,52}
2) B={13,17,47}

Also, questions involving the Common Mistake Type 4(A) is very tricky.
(ex 2) A, B are two sets whose elements are integers, A∪B represent union set of two sets A, B. Is each of the elements in the set A divisible by 3?
1) A∪B={13,17,31,47,52}
2) B={13,17,47}
Answer: A

There are questions that involve both the common mistake type 1 (no is also an answer) and the common mistake type 4(A). In above question, C is also an answer. If we look at that condition 1), even if A’s elements are any numbers, it cannot be divided by 3. The answer is no and the condition is sufficient. Therefore, the correct answer is A.
This is a type of questions that appears in 50-51.

Also, there are statistics questions that involve the Common Mistake Type 4(A).
There are two kinds of books: hard-covers and paper-covers, if the range of the prices of both kinds of books is $50 and the range of the prices of paper-cover is $10, what is the range of the prices of the hard-cover books?
1) The lowest price of hard-cover books is $2 less than the highest price of paper-cover.
2) The highest price of hard-cover books is $40 more than the highest price of paper-cover books.
Answer: A

There are 4 variables and 2 equations. Hence, C can be an answer but since this is a statistic question, one of key questions, we need to apply the Common Mistake Type 4(A). The condition 1) is sufficient by itself, and the correct answer is A. You need to be strong at this type of questions to get 51.

As mentioned above, questions related to Murphy’s Law and Sally’s Law might appear in the GMAT test.
You need to get them right if you are aiming for the perfect 51!

As always, there are questions that is combined with the common mistake type 3 and 4. Let’s take a look at a question below. This is a 50-51 level question and is a question that involves the common mistake type 4(A). You need to be strong at these questions and have to know the relationship between the Variable Approach method and the Common Mistake Types.

If x, y, and z are integers greater than 1, x+y+z=?
1) xyz=154
2) x-y-z=2

There are 3 variables (x,y,z) in the original condition. In order to match the number of variables to the number of equations we need 3 equations. Hence, there is high chance that E is the answer. Using both the condition 1) and the condition 2), we get 11, 2, 7. The answer is unique and the condition is sufficient. Hence, the correct answer MIGHT be C.
However, since this is one of key questions, integer question, we need to apply the common mistake type 4(A). If we use the condition1 ), we get 11,2, 7. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

Be careful on probability questions.
2 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
A. 12 B. 15 C. 18 D. 21 E. 24

Answer: A

Since, 3!*2!=12, the answer is A. This is a type of questions that appear in the 50-51 range.

You also need to be careful on probability questions that involve “at least” like below.
In a certain factory the production line which produces the bulbs has the probability that a bulb selected at random is defective is 0.01. If 10 bulbs are selected at random, what is the probability that at least one bulb is defective?
A. 0.0110 B. (0.01)(0.99)10 C. 1-(0.01)10 D. 0.9910 E. 1-(0.99)10

Answer: E
Since the question asks what is the probability of 10 bulbs, selected at random, are all “no defective”, the answer is E.

Also, there is a statistic question like below.
If the heights’ range of men is 14 inches and the heights’ range of women is 10 inches, what is combined heights’ range?
1) The shortest man is 3 inches shorter than the tallest woman.
2) The height of highest man is 72 inches.
Answer:A
There are 4 variables and 2 equations (14=MT-Ms, 10=WH-WS), in the original condition. In order to match the number of equations and the number of variables, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and the condition 2), C is the answer. However, this is a statistic question, one of the key questions. Hence, we need to apply the Common Mistake Type 4(A). We can see the condition 1) is sufficient by itself, making A and correct answer. Be careful on this type of question.

There are many probability questions nowadays. You should be careful on these questions.
A certain jar has total 8,000 red marble, blue marbles, and green marbles. And the red marbles’ number is twice the blue marbles’ and the green marbles’ number is 20 more than the sum of red and blue marbles. If one marble is selected from randomly the jar, what is the probability that marble selected is red?
A. 133/400 B. 131/400 C. 129/400 D. 127/400 E. 137/400
Answer: A

Also, When (10^100)^20 have n consecutive 0-digits from units digit, what is the greatest possible value of n?
A. 1040 B. 10400 C. 1002 D. 1020 E. 10400
Answer: A
This is a PS question but in the score range of 50-51. Since 100^20=10^40, the correct answer is A.

if xy+z=x(y+z), which of the following must be true

1 x=0 & y=0


2 x=0 & y=1

3 y=1 & z=0

4 x=1 & y=0

5 x=1 & z=0

From GMAT prep mock

Below is another 50-51 question.
On the number line m, s, t are there. If t and m are positive, is m=t?
1) |t-s|=|m-s|
2) s<0
Answer: C
There are 3 variables in the original condition (m, s, t). In order to match the number of variables and the number of equations, we need 3 equations. Hence, there is high chance that E is the correct answer. Using the condition 1) and the condition 2), the absolute values designates the distant between two points. Hence, the correct answer is C.

If x is an integer less than 11 and n is a positive integer, is x a prime number?
1) x2=n!+1
2) x=2n+1
Answer: A
This is also a 50-51 level question. There is 1 variable (x) in the original condition and there is high chance that D is the answer.
For the condition 1), n=4(x=5), n=5(x=11), the answer is always yes, and the condition is sufficient.
For the condition 2), x=5 yes, x=9 no. The condition is not sufficient, and the correct answer, thus, is A. This would be the hardest level question among 50-51 level questions.

It is well-known that the way to find out approximation value of a positive integer n’s square root is following;
1st approximation: select a positive integer "a" and n is divided by a.
2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor.
What is the approximation positive integer n’s square root, in terms of a and n?
A. (a2+n)/2a B. (a2+n)/2 C. (a2-n)/2a D. (a2+n)/a E. (a2+2n)/a
Answer: A

This is a thesis=like question. It is a very challenging 50-51 level question. N=aQ means √n=(a+Q)/2. Hence, the correct answer is A.