The Ultimate Q51 Guide [Expert Level]

As always, advanced questions like combined questions of the mistake type 3 and 4 are frequently given. Let's have a look at the recent question. It also belongs to the mistake type 4(A), which is at level of score 50-51. You have to be strong on this type of question and know the relation between method of variable approach and the mistake types.

(ex 1) If x, y are integers, is x^2+9x+y an even number?

1) x=15
2) y=10

Answer: B


In this question, not only is C the answer but also B, which is a typical question at level of score 50-51. You should be able to tackle a question like this. Focus on integer or statistics questions, which make C the answer.

In addition, the mistake type 4(A) questions related to our life are given at level of score 50-51. In a case of the question below, the answer is A if you modify the question.

(ex 3) Machine X is taken 30 minutes for preparing to work and machine Y is taken 20 minutes for warming up before driving machines. The work rate of machine X is 40 parts per 1 minute and machine Y is 30 parts per 1 minute. Is the total time taken to work including preparing time of machine X smaller than that of machine Y?

1) The total task is more than 1,200 parts.
2) The total task is less than 1,800 parts.


Therefore, when you face with questions related to real life, approach them very cautiously.

As always, questions combined with the mistake type 3 and 4 are evolving and often given. The below question is recent, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to solve this type of question and know the relation between method of approach to variables and the mistake types.

(ex 1) If x and y are different prime numbers, and n is a positive integer, what is the factors’ number of x(y^n)?

1) xy=21
2) n=2

Answer: B


The answer is C but also B, which is a typical question at level of score 50-51. You have to be strong with a question like this. Be cautious on integer or statistics questions, which make C the answer. Especially, be aware of the word "different" when questions with factor or prime factors are given.

In addition, questions of the mistake type 4(A) related to method of approach to variables 1st account for considerable parts of scoring. C can also be the answer of the question below.

(ex 2)8^(s+3r)/4^(2s+5r)=?

1) s+r=3
2) 2s-r=6

Answer: A


In a case like this, when you modify the question, 2^(-s-r)=0? is derived. For 1), s+r=3, which is sufficient and the answer. is A.
This type of question is always at level of score 50-51.

Besides, questions trembling students like the below still have been given on exams. The below question adapts the concept of an absolute value is an length of two points. This type of question has continuously appeared since 10 years ago. Sure, as there are 3 variables, the answer is E.

(ex 3) Is |x-y|<|x-z|?
1) |y|<|z|
2) x<0
Answer: E


It might look simple seemingly though it can be overwhelming when you actually face it in an exam. Approach this type of question after fully comprehending the method of approach to variables.

As always, more developed questions combined with the mistake types 3 and 4 appear on GMAT. Look at the question below. This is a very recent one, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to tackle this type of question. Be aware of a relation between the method of approach to variable and the mistake types.

(ex 1) What is the median of 5 numbers?
1) They have 5 and 15
2) 3 of them are 10 each

Answer: B

In this question, the answer is C but also B, which is a typical question at level of 50-51. You have to be strong with this type of question. Focus on integer or statistics questions that make C the answer.

Geometry questions are continuously increasing. Let's have a look at the recent question below.


A cube has 4 as a side’s length. If A and B are midpoints of each side and C is a vertex of the cube, what is the length of AB?
A. 2√3
B. 3√6
C. √6
D. 3√2
E. 2√6

Answer: E

In a case of this question, you can just use Pythagoras' theorem twice. This type of geometry questions are likely to have been increasing since 2014. If AC^2=2^2+4^2=20, AB=x, x^2=2^2+AC^2=24 is derived. Then, x= √24= 2√6.
The answer is E.

As usual, developed questions combined with the mistake types 3 and 4 appear on GMAT. Let's look at the question below. This is a recent question, which also belongs to the mistake type 4(A) at level of score 50-51. You have to excel at the question like this, and also comprehend the relation between method of variable approach and the mistake types.

(ex 1) Is the range of a, b, c, and d greater than 7?
1) c-a=4, a-d=4
2) c-b=7

Answer: A


The answer is C but also A, which is a typical question at level of score 50-51. You should focus on integer or statistics questions that make C the answer.

Also, this question is related to the mistake type 4(A). In this case, when number and ratio are given in a question, it is most likely that ratio can be the answer.

(ex 2)A certain company sells pencils in package and its sale price is not changed for a special sales period. But if the pencils’ number in one package is reduced, by what percent the unit sale price of pencils in one package increased?

1) The sale price per one package is $8
2) The reduced number of pencils in one package is 20 percent of the original number

Answer: B

In this case, B which is ratio is the answer. This type of question is at level of score 50-51

As always, more developed questions combined with the mistake types 3 and 4 appear on GMAT. Look at the question below. This is a very recent one, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to tackle this type of question. Be aware of a relation between the method of approach to variable and the mistake types.

(ex 1) What is the median of 5 numbers?
1) They have 5 and 15
2) 3 of them are 10 each

Answer: B

In this question, the answer is C but also B, which is a typical question at level of 50-51. You have to be strong with this type of question. Focus on integer or statistics questions that make C the answer.

As always, more developed questions combined with the mistake types 3 and 4 appear on GMAT. Look at the question below. This is a very recent one, which also belongs to the mistake type 4(A) at level of score 50-51. You should be able to tackle this type of question. Be aware of a relation between the method of approach to variable and the mistake types.

(ex 1) What is the median of 5 numbers?
1) They have 5 and 15
2) 3 of them are 10 each

Answer: B

In this question, the answer is C but also B, which is a typical question at level of 50-51. You have to be strong with this type of question. Focus on integer or statistics questions that make C the answer.

Plus, this highly advance question is related to daily life. You also should be able to tackle PS questions.

There are 4 bottles with the same number balls m respectively. If balls from the only 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls of the bottles is 1 to 6 to 5 to 4, does the moved balls represent in terms of m?

A. m/4 B. m/2 C. 3m/4 D. m E. 4m/5

Answer: C


It might seem simple though this can be very burdensome. You shouldn’t deal with PS question with disregard.

In addition, integer questions are still frequently given.
Let's have a look at the question below.

(ex 5) If the first 20 positive even numbers’ sum is 420, what is the first 20 positive odd numbers’ sum?

A. 210
B. 240
C. 320
D. 360
E. 400

Answer: E

-> Even numbers are always bigger by 1 and there are 20 of them, which makes a difference by 20.
Thus, the answer is 400.

Furthermore, the below question is an advanced question related to real life. You also have to be strong with a PS question like this.

(ex 3) one apple is 1pound per $1. If the apple is peeled off and cored, 1/5 of the original apple's weight is off. Then the peeled and cored apple can be apple pie and 2cups of apple juice made by a blender come from such apple 1 pound. If such 3 cups of apples juice can make one apple pie, how much money it needs to make p apple pies, in dollars?

A. 2p
B. 15p/8
C. 8p/15
D. 2p/3
E. 3p/2

Answer: B

It might seem simple, but it can be challenging when you actually face this type of question on actual GMAT

Moreover, highly advanced integer questions are frequently given.

(ex) For positive integers n, k, f(n) is the remainder when n is divided by k. Is k>10?

1) f(k+32) = 8
2) f(k+42) = 6

Answer: A

In this case, the answer is B. You must have a solid concept of integer questions.
For 1), k=12,24 -> always yes and sufficient.
For 2), k=9 no, 12 yes -> not sufficient.

Hence, the answer is A.

Also, highly advance integer questions are frequently given.

We define “A mod n” as the remainder when A is divided by n. What is the value of “A mod 6”?

1) A mod 3=A mod 12
2) A mod 4=2

Answer: C

In this case, the answer is C. You have to have a solid concept of integer questions.
For 1), A mode 6=1,2, it is not unique and not sufficient.
For 2), A mode 6=0,2, it is not unique and not sufficient.
When 1) & 2), only A mode 6=2 is derived, which is unique and sufficient.
Hence, the answer is C.

As always, there are some advanced questions that are combined with the Common Mistake Type #3 and #4. Let’s have a look at the example below. This is a very recent type of questions, which also belongs to the mistake type 4(A). Since such types of questions appear in the level of score 50-51, you should be able to get them right for high scores. To this end, you should be aware of the relationship between the Variable Approach Method and the Common Mistake Types.
If the average (arithmetic mean) height of John, Tom and Jack is 1.70m, what is the median height of them?

1) The height of Tom is 1.65m.
2) The height of Jack is 1.70m
Answer:B

The answer to the above question is C but also B at the same time. This is a typical question that appears in the level of score 50-51. For high scores, you should be able to tack these types of questions. Focus on integer or statistics questions, which can make C an answer!