Quant Question of the Day Chat

PS Question 1 - Jan 01

What is the range of the roots of ||x–1|–2| = 1 ?

A. 0
B. 2
C. 4
D. 6
E. 8

Source: GMAT Club Tests | Difficulty: Medium

DS Question 1 - Jan 01

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

Source: Official Guide | Difficulty: Hard

PS Question 1- Jan 02

A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?

A) 3
B) 4
C) 5
D) 6
E) 7

Source: Veritas Prep | Difficulty: Medium

DS Question 1 - Jan 02

Does the integer g have a factor f such that 1 3!
(2) 11! + 11 >= g >= 11! + 2

Source: Veritas Prep | Difficulty: Medium

Spent way longer on this, because I didn’t trust my analysis
Answer should be B.
1) Is clearly insuff. Can be rewritten as g>6, if g=7 no, if g=8 yes.

2)
It is possible to find some number between 2-11 that g is divisible by.
for example, if g=11!+3, g will be divisible by 3 since 11! contains all numbers from 1 to 11.
Because g is integer (given in stem) we can do the same for all possible values of G. Therefore, sufficient.

DS Question 1 - Jan 03

The median age of 15 children in group A was 12. The median age of 19 children in group B was 9. Two children - the youngest and the oldest - in group B were to group A. What was the new median age of the children in group A?

(1) The youngest children in group B was 7 years old.
(2) The oldest child in group B was 12 years old.

Source: Experts Global | Difficulty: Hard

PS Question 1 - Jan 03

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Source: Official Guide | Difficulty: Hard

There are probably better ways to do it, but:

From stem we can derive that Rate(x)=w/t+2 and Rate(y)=w/t
now
(w/t+2)+(w/t))3=5w/4

2t+2/(t^2+2t)=5/12

12(2t+2)=5(t^2+2222t)
0=5t^2-14t-24
0=(5t+6)(5t-4)
t=-6/5 or t=4
Clearly, rates cannot be negative so t=4

Plugging back into first equation, it takes X (4+2)=6 days to produce W widgets, therefore it must take 12 to produce 2w.

For tricky algebra questions like this, I recommend using the answer choices to guide the way you pick numbers


Did very little calculations and went by pure logic:

1) Even if we know the age of the youngest child, we cannot conclude how the set will change.
We could have, for example, everyone being the age 12 and the median would be unchanged.
But it could also be the case that element 8 in the set was 12, and element 9 in the set was 15. If that is the case, the new median cannot be determined. Ins.

2) If the oldest of B was 12, then we have added 1 more element in Set A which is the same as the median. So no matter what, we will have the original 12 in position 8 in the first set, and the second 12 will be, in the worst case, position 9. The median will therefore always be 12 after the change in set A.
Sufficient.

B


Note that this logic is only possible because A is originally a set with an odd number of elements - the element 12 must be in the actual set itself for it to be the median. If it the number of elements were even, you could not use this logic

DS Question 1 - Jan 04

If (ax + by)^2 = (bx + ay)^2, what is the value of a – b ?

(1) x^2 > y^2

(2) a and b are positive integers.

Source: Manhattan | Difficulty: Hard

PS Question 1 - Jan 04

A student’s grade in a college course is determined by the scores of 5 quizzes, a midterm exam and a final exam. The midterm exam and the final exam both count twice as much as a quiz in determining the student’s average grade. If the student averages a score of 80 on the quizzes and scored a 90 on the midterm exam, then what would the student have to score on the final exam to have an overall average grade of 85 for the entire course?

A - 85.5
B - 90
C - 92.5
D - 93.5
E - 95

Source: EMPOWERgmat | Difficulty: Medium

DS Question 1 - Jan 05

If m and n are prime numbers, what is the value of |m-n|?

(1) m + n is a prime number.

(2) Both m and n are less than 5.

Source: Others | Difficulty: Hard

PS Question 1 - Jan 05

If 0.00012345 is between 1/(10^n) and 1/10^(n−1), what is the value of integer n?

A. 2
B. 3
C. 4
D. 5
E. 6

Source: Math Revolution | Difficulty: Medium

DS Question 1 - Jan 06

Is the product of three consecutive integers negative?

(1) The sum of the integers is equal to the product of the integers.
(2) At least one of the integers is negative.

Source: GMAT Club Tests | Difficulty: Hard

This is sneaky.

Statement 2) If at least 1 is negative, we can have a few cases:
Case 1, where -1,0,1 (0 is non-negative)
Case 2, where -2,-1, 0 (0 is non-negative)
Case 3, where -3,-2,-1 (or any other combo of 3 negative integers, which is always negative)

Statement 1) We can have -1,0,1, in which case it is not negative. We can have also the case 3 from before, -3,-2,-1, which is negative.

1+2) Clearly we have 2 repeat cases with different answers. Must be E.

PS Question 1 - Jan 06

Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

A. 20
B. 25
C. 30
D. 35
E. 40

Source: GMAT Club Tests | Difficulty: Hard

Interesting Q.
Assume that x people read A, and y people read B.
We are told that
20% of X read A and B, and 25% of Y read B and A.
This means that:
1/5x=1/4y
4x=5y
We are also that each student has read at least 1 book. This means that there are no students who have read neither.
We can now set up the equation:
x+y-both+neither=200
We can solve for either x or y, lets solve for X
y=4x/5
4x/5+x-1/5x+0=200
x=125
y=100
Now we can solve for only x and only:
25 people read both x and y, so only Y is 75, and only X is 100.
The difference between the two is 25, which is the answer.
B

Hello, is there any Quant mini book that has all the tricks and details I can use for different questions?

We have a maxi-size only 😬😇

there are a few resources, however, that may be more along the lines of what you were thinking about

1. GMAT Flashcards: gmat-flashcards-108651.html

2. what-arithmetic-should-i-memorize-80128.html

3. Not what you are looking for by a far stretch but perhaps something useful inside of the Quant Megathread: ultimate-gmat-quantitative-megathread-244512.html

Can someone help me to solve this problem ?

Yes correct, but how you do it ?

|(D(n) - D(n-1) )|/ D(n-1) highest value of this fraction will be the answer.

While you can find the percentage change for each options, I would recommend you do some observations and limit the number of options to test.

What observations can we make ?

Between the subsequent graphs, the change is either of three levels (6 points) or of four levels (8 points).
Now the percentage shift will be - change divided by the value of the previous level .
Hence, lower the value of the previous level, greater the percentage change will be.

Now, let’s see what the change is between the subsequent graphs

1 & 2 ⇒ Change : 4 levels ( or 8 points) | Previous Point ⇒ 20
2 & 3 ⇒ Change : 3 levels ( or 6 points) | Previous Point ⇒ 12
3 & 4 ⇒ Change : 4 levels ( or 8 points) | Previous Point ⇒ 18
4 & 5 ⇒ 3 levels ( or 6 points) | Previous Point ⇒ 10
5 & 6 ⇒ 4 levels ( or 8 points) | Previous Point ⇒ 16

Among all the changes, the greatest change can only be between either 4 & 5 or 5 & 6. This is because for the same level change the previous point is least for these two cases.

Hence we only need to test option D and option E and level the rest.

Option D = 6/10 = 0.6 (or 60%)
Option E = 8/16 = 0.5 (or 50%)

Hope this makes sense !

Realized there is a typo : level the rest ⇒ leave the rest

DS Question 1 - Jan 07

Is m +n^3 odd?

1) m is odd and n is even
2) m-n is odd

Source: Others | Difficulty: Hard

PS Question 1 - Jan 07

The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

(A) 1,350π
(B) 1,200+400π
(C) 1,200+300π
(D) 1,200+200π
(E) 1,200+150π

Source: Official Guide | Difficulty: Medium