Quant Question of the Day Chat

thnx, gmatophobia ☺️

Question of the day

Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares that Fritz owns is 2/3 of number of the shares of the other three shareholders, number of the shares that Luis owns is 3/7 of number of the shares of the other three shareholders and number of the shares that Alfred owns is 4/11 of number of the shares of the other three shareholders. If dividends of $3,600,000 were distributed among the 4 shareholders, how much of this amount did Werner receive?

A. $90,000
B. $100,000
C. $120,000
D. $180,000
E. $240,000

Difficulty Level: Hard | Source: GMAT Club Tests

Problem Solving Question - Quant Butler

If x and y are integers such that 4x^2 – y^2 +4x + 4y – 3 = 0, which of the following must be true?

A. y is an even number.
B. y is an odd number.
C. y is positive.
D. y is negative.
E. y is a prime number

Source: Math Revolution | Difficulty: Medium

Problem Solving Question - PS Butler

If (6^3)a + (6^2)b + 6c + d = 821, where a, b, c, and d are integers from 0 to 5, inclusively, what is the value of c ?

A. 0
B. 1
C. 2
D. 3
E. 4

Source: Math Revolution | Difficulty: Medium

Weekend is here and also the topic of the day

Topic of the day: IMO Number line is a very powerful technique to solve some of tricky GMAT Quant questions. The use of number line provides good visualization especially in data sufficiency question, reducing chance of silly mistakes. So here’s the topic of the day folks -

4 Regions on a Number Line
Posted By : GMATWhiz

Weekend is here and also the topic of the day

Topic of the day IMO Number line is a very powerful technique to solve some of tricky GMAT Quant questions. The use of number line provides good visualization especially in data sufficiency questions, reducing chance of silly mistakes. So here’s the topic of the day folks -

Link: 4 Regions on a Number Line
Posted By : GMATWhiz

Data Sufficiency - Question 1

If q, s, and t are all different numbers, is q q

Source: Official Guide | Difficulty : Medium

Here is my take on this question.

We want to know if q ,s, and t can be represented as shown below on the number line

---q---s---t---

Note: We don’t know at what position does 0 lie on the number line.

1) t - q = |t-s| + |s-q|

We can conclude that t - q is a positive value* as it is represented as sum of two modulus operation.

So, t lies to the right of q on a number. When represented on a number line

---q--------t----

Also we know that the distance between t and q is the sum of distance between t and s and the distance between s and q. So the only way this is possible is when s is in between q and t.

----q----s----t---

This is exactly what we need to find.

So St1 is sufficient

2) t lies to the right of q on a number line. However we do not know the position of s, hence not sufficient.

Answer : A

* : t - q cannot be zero as the numbers are different.

Side Thought: B doesn’t say anything different than Statement 1 does. Both statement provide us with the information that ’t’ lies to the right of ’q’. So if A were not sufficient then both combined would also not be sufficient. Hence the answer cannot be C.




Data Sufficiency - Question 2

What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0

Source: Manhattan GMAT | Difficulty : Medium

Hint : We know that the difference of two distances is 6. So the numbers can lie either on the same side of number line on on opposite sides .

Typo: or on opposite sides*

Yes missed one particular condition, its c👍👍

Thanks

Data Sufficiency - Question 3

Is x > y ?

(1) root(x) > y

(2) x^3 > y

Source: Manhattan GMAT | Difficulty : Hard*

*Medium if you use number line to solve this

Would love to see some responses to this

Data Sufficiency - Question 4

On a number line, the distance from point A to zero is greater than the distance from point B to zero. Does point C lie between points A and B on the number line?

1) ABC > 0
2) |A| > |B| > |C|

Source: EMPOWERgmat | Difficult: Hard

E

since A and C could be negative and B positive, in which case C would lie in between. But on the other hand, A and B could be negative and C positive in which case C wouldn’t lie in between


C. With statement 1, X could be a positive fraction or greater than one - in both cases the answer would be different. With statement 2, x could be negative fraction or greater than 1. But combining both we know that it has to be greater than one on the number line, in which case it will be greater than y.

PS Question of the day

N = 10^{40} + 2^{40}. 2^k is a divisor of N, but 2^{k+1} is not a divisor of N. If k is a positive integer, what is the value of k-2 ?

A) 38
B) 39
C) 40
D) 41
E) 42

Source: GMATPrepNow | Difficulty: Hard

Answer: B

10^40 + 2^40 = 2^40 {5^40 + 1}

Now, 5^40 + 1 will end in Units Place of 6 which is also divisible by 2 so we will have

= 2^41 {Some expression} => k = 41, so k-2 = 39

==2

DS Question for the day

The numbers D, N, and P are positive integers, such that D < N, and N is not a power of D. Is D a prime number?

(1) N has exactly four factors, and D is a factor of N
(2) D = (3^P) + 2

Source: Magoosh | Difficulty: Hard