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# Quant Question of the Day Chat

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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 2 - Jan 14 If at least one of p, q, r is an integer, is p+q+r even? (1) p−q−r is even. (2) (p-r)/q is odd Source : Others | Difficulty: Hard

statement 1:
p-q-r = even
we dont have any confirmation that even if all of them is not an integer, subtraction gives an even integer but sum of these dont haver to be an integer and hence we cant comment on the nature of the sum of these numbers.
3.52 - 0.02 - 1.50 = 2 even
3.52 + 0.02 + 1.50 = 5.04 not an integer

Statement 2:
(p-r)/q = odd
say, (8-3)/0.20 = 25
but, 8+3+0.20 = not integer

even we combine the statement we still cant be sure if sum p+q+r will land as an integer, hence we can’t really comment on odd/even nature of that sum.

with this note - going for option E
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Re: Quant Question of the Day Chat [#permalink]
Adding to Abhinavs points, considering them together.
We can take p=7.55, q= 1.5, r= 0.05
p-q-r = 4
(p-r)/q= 5
p+q+r = not an integer

p= 7, q= 2,r = 5
p-q-r = 0
(p-r)/q = 1
p+q+r =14

Not sufficient

E
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Jan 14 What is the value of xy? (1) 3^x ∗ 5^y = 75 (2) 3^[(x−1)(y−2)] = 1 Source : GMAT Club Tests | Difficulty: Hard

C

gmatophobia wrote:
DS Question 2 - Jan 14 If at least one of p, q, r is an integer, is p+q+r even? (1) p−q−r is even. (2) (p-r)/q is odd Source : Others | Difficulty: Hard

E

DS Question 1 - Jan 15

If 15 is a factor of p as well as q, is 15 the highest common factor of p & q?

1. q=3p.
2. q-2p=15.

Source: Expert’s Global | Difficulty: Medium

PS Question 1 - Jan 15

An auditor wants to conduct audits in 4 schools, of 5 different cities, in such a way that no two schools belong to same city. If in each city, there are 2 schools then in how many ways can the auditor select the schools for audit?

(A) 10
(B) 20
(C) 40
(D) 80
(E) 160

Source: GMATWhiz | Difficulty: Medium

Originally posted by gmatophobia on 15 Jan 2023, 00:10.
Last edited by gmatophobia on 15 Jan 2023, 00:22, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Jan 15 If 15 is a factor of p as well as q, is 15 the highest common factor of p & q? 1. q=3p. 2. q-2p=15. Source: Expert’s Global | Difficulty: Medium

question stem: common factor 15 exists for both p and q, but is 15 the HCF ?

statement1:
q=3p

say, q = 15a = 3*5*a
say, p = 15b = 3*5*b
we don’t know if "a, b" can have common factors, if they do 15 is not HCF if "a, b" don’t have common factors then 15 is the GCD. No straight answer.
So insufficient

statement2:
q-2p=15
q=15+2p

again say:
q = 15a
p = 15b

substituting above and killing "15":

15a=15+2(15b)
=> a=1+2b

the above relation shows that a,b can’t have common factors between them; they are co-primes
b=2,1,10,21
a=5,3,21,43 .. so on

Then we get that p and q that has "15" as common factors, are the HCF for them as well.

Option B
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Jan 15 If 15 is a factor of p as well as q, is 15 the highest common factor of p & q? 1. q=3p. 2. q-2p=15. Source: Expert’s Global | Difficulty: Medium

1)CASE 1- q= 15
p= 5
HCF - 5
CASE 2- q= 45
p=15
HCF- 15
Not Sufficient
2) q-2p =15
Case 1 p= 5
q= 25
HCF =5
Case 2
p= 15
q=45
HCF HCF - 15
Not sufficent

Together
Substitute q =3p in 2
We get p=15
q= 45
Hence HCF - 15
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Re: Quant Question of the Day Chat [#permalink]
2. There are 5C4 ways of selecting the city, 2C1 ways of selecting a school in a particular city.

Therefore number of ways of selecting schools for the audit is
5×2×2×2×2 =80
D) 80
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Jan 15 If 15 is a factor of p as well as q, is 15 the highest common factor of p & q? 1. q=3p. 2. q-2p=15. Source: Expert’s Global | Difficulty: Medium

B

gmatophobia wrote:
PS Question 1 - Jan 15 An auditor wants to conduct audits in 4 schools, of 5 different cities, in such a way that no two schools belong to same city. If in each city, there are 2 schools then in how many ways can the auditor select the schools for audit? (A) 10 (B) 20 (C) 40 (D) 80 (E) 160 Source: GMATWhiz | Difficulty: Medium

D

DS Question 1 - Jan 16

In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon?

1) One of the triangles has an area of 12.
2) All the sides of the hexagon are of equal length.

Source: 800 Score | Difficulty: Hard

PS Question 1 - Jan 16

Which of the following expressions yields an even integer for any integer n?

A. n^2−10n+21
B. n^2−2n−24
C. n^2+8n+7
D. n^2+11n+18
E. n^2−4n−60

Source: Others | Difficulty: Medium

Originally posted by gmatophobia on 16 Jan 2023, 00:45.
Last edited by gmatophobia on 16 Jan 2023, 00:55, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Jan 16 Which of the following expressions yields an even integer for any integer n? A. n^2−10n+21 B. n^2−2n−24 C. n^2+8n+7 D. n^2+11n+18 E. n^2−4n−60 Source: Others | Difficulty: Medium

D

gmatophobia wrote:
DS Question 1 - Jan 16 In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon? 1) One of the triangles has an area of 12. 2) All the sides of the hexagon are of equal length. Source: 800 Score | Difficulty: Hard

Its E, we don’t know the internal distance even if the sides are the same

Originally posted by mysterymanrog on 16 Jan 2023, 01:08.
Last edited by mysterymanrog on 16 Jan 2023, 01:10, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Jan 16 In the figure above, three segments are drawn to connect opposite vertices of a hexagon, forming six triangles. All three of these segments intersect at point A. What is the area of the hexagon? 1) One of the triangles has an area of 12. 2) All the sides of the hexagon are of equal length. Source: 800 Score | Difficulty: Hard

E

gmatophobia wrote:
PS Question 1 - Jan 16 Which of the following expressions yields an even integer for any integer n? A. n^2−10n+21 B. n^2−2n−24 C. n^2+8n+7 D. n^2+11n+18 E. n^2−4n−60 Source: Others | Difficulty: Medium

D

DS Question 1 - Jan 17

{a, b, c, d}
What is the mode of the list above?

(1) The product of no two elements of the list is positive
(2) The range of the elements of the list is 0

Source: GMAT Club Tests | Difficulty: Hard

PS Question 1 - Jan 17

Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet?

A. 135 miles
B. 90 miles
C. 70 miles
D. 65 miles
E. 25 miles

Source: GMAT Club Tests | Difficulty: Medium

Originally posted by gmatophobia on 16 Jan 2023, 23:57.
Last edited by gmatophobia on 17 Jan 2023, 00:00, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Jan 17 Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet? A. 135 miles B. 90 miles C. 70 miles D. 65 miles E. 25 miles Source: GMAT Club Tests | Difficulty: Medium

total separation = 360 miles
Both are moving towards each other, relative speed = 25+65 = 90 mph
so they meet after 360/90 hr = 4 hr
but, 1.5 hr before they meet, they travelled distance = 90 * (4 - 1.5) miles = 225 miles

so, distance beteem them remains = 360-225 = 135 miles

Option A

gmatophobia wrote:
DS Question 1 - Jan 17 {a, b, c, d} What is the mode of the list above? (1) The product of no two elements of the list is positive (2) The range of the elements of the list is 0 Source: GMAT Club Tests | Difficulty: Hard

Statement1:
{a,b,c,d} product of no two numbers is "positive"
so all number can be "0"
or 3 numbers are zero, the last number is any number
or 2 numbers are zero, rest two are opposite sign number

the mode in all case is "0" as it appears most often in any of the above combination
(1) seems Sufficient statement

Statement2:
range of set is zero

now any of these cases are possible:
{34,34,34,34}
{-6,-6,-6,-6}
{2,3,5,5} ... so on

we don’t have a fix which number will be treated as mode
so, insufficient statement

going with option A ?

PS : {2,3,5,5} is an invalid example! , ignore it

Originally posted by AbhinavKumar on 17 Jan 2023, 00:24.
Last edited by AbhinavKumar on 17 Jan 2023, 00:40, edited 4 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Jan 17 Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet? A. 135 miles B. 90 miles C. 70 miles D. 65 miles E. 25 miles Source: GMAT Club Tests | Difficulty: Medium

A

gmatophobia wrote:
DS Question 1 - Jan 17 {a, b, c, d} What is the mode of the list above? (1) The product of no two elements of the list is positive (2) The range of the elements of the list is 0 Source: GMAT Club Tests | Difficulty: Hard

A

PS Question 1 - Jan 18

If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetlana, respectively, then Pat will have one fourth as many bitcoins as will Svetlana, who will in turn have twice as many bitcoins as will Juanita. If Pat currently has 2 bitcoins, then how many more bitcoins does Juanita currently have than Svetlana?

A. 8
B. 12
C. 20
D. 22
E. 24

Source: Kaplan | Difficulty: Medium

DS Question 1 - Jan 18

What is the value of x?

(1) x^2-10x=24

(2) 4x/(x^2-2x)=2/5

Source : GMATPrepNow | Difficulty : Hard Tricky

Originally posted by gmatophobia on 17 Jan 2023, 23:30.
Last edited by gmatophobia on 17 Jan 2023, 23:34, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
DS Question 2 - Jan 18[b]

Is rectangle R a square?

(1) At least one side of rectangle R has an integer length.

(2) The diagonals of rectangle R have integer lengths.

Source: Manhattan | Difficulty : Medium

[b] DS Question 2 - Jan 18

Is rectangle R a square?

(1) At least one side of rectangle R has an integer length.

(2) The diagonals of rectangle R have integer lengths.

Source: Manhattan | Difficulty : Medium

Originally posted by gmatophobia on 18 Jan 2023, 00:57.
Last edited by gmatophobia on 18 Jan 2023, 00:58, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Jan 18 If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetlana, respectively, then Pat will have one fourth as many bitcoins as will Svetlana, who will in turn have twice as many bitcoins as will Juanita. If Pat currently has 2 bitcoins, then how many more bitcoins does Juanita currently have than Svetlana? A. 8 B. 12 C. 20 D. 22 E. 24 Source: Kaplan | Difficulty: Medium

Juanita is rich by 8 bitcoins !
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Re: Quant Question of the Day Chat [#permalink]
1
Bookmarks
gmatophobia wrote:
DS Question 2 - Jan 18 Is rectangle R a square? (1) At least one side of rectangle R has an integer length. (2) The diagonals of rectangle R have integer lengths. Source: Manhattan | Difficulty : Medium

C

gmatophobia wrote:
PS Question 1 - Jan 18 If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetlana, respectively, then Pat will have one fourth as many bitcoins as will Svetlana, who will in turn have twice as many bitcoins as will Juanita. If Pat currently has 2 bitcoins, then how many more bitcoins does Juanita currently have than Svetlana? A. 8 B. 12 C. 20 D. 22 E. 24 Source: Kaplan | Difficulty: Medium

A

gmatophobia wrote:
DS Question 1 - Jan 18 What is the value of x? (1) x^2-10x=24 (2) 4x/(x^2-2x)=2/5 Source : GMATPrepNow | Difficulty : Hard Tricky

B

DS Question 1 - Jan 19

The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is odd

(2) n >= 9

Source: Others | Difficulty: Hard

PS Question 1 - Jan 19

If a and b are both factors of 50, which of the following must be true?

(A) ab≥ 2
(B) a + b≤ 50
(C) ab is a factor of 100.
(D) ab is a factor of 2500.
(E) ab is even.

Source: Kaplan | Difficulty: Hard

Originally posted by gmatophobia on 18 Jan 2023, 23:16.
Last edited by gmatophobia on 18 Jan 2023, 23:22, edited 3 times in total.
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Re: Quant Question of the Day Chat [#permalink]
1
Bookmarks
PS Question 1 - Jan 21

If a^(1/2) > b > c^2, which of the following could be true?

I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Source: Expert’s Global | Difficulty: Hard

DS Question 1 - Jan 21

The average (arithmetic mean) cost of three computer models is \$900. If no two computers cost the same amount, does the most expensive model cost more than \$1,000?

(1) The most expensive model costs 25% more than the model with the median cost.
(2) The most expensive model costs \$210 more than the model with the median cost.

Source: Manhattan GMAT | Difficulty: Hard

Originally posted by gmatophobia on 21 Jan 2023, 02:32.
Last edited by gmatophobia on 21 Jan 2023, 02:33, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
DS Question 1 - Jan 23

The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

(1) The perimeter of the rectangle is 84
(2) The shorter side of the rectangle is 2

Source: GMATClub Tests | Difficulty: Medium

PS Question 1 - Jan 23

Among the customers who bought either tables or chairs at a certain furniture store, the ratio of customers who bought tables to customers who bought chairs is 3:2. If half of those who bought chairs also bought tables, what percent of customers bought tables?

A. 60%
B. 65%
C. 70%
D. 75%
E. 80%

Source: Veritas Prep | Difficulty: Hard

Originally posted by gmatophobia on 23 Jan 2023, 02:32.
Last edited by gmatophobia on 23 Jan 2023, 02:34, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Jan 23 Among the customers who bought either tables or chairs at a certain furniture store, the ratio of customers who bought tables to customers who bought chairs is 3:2. If half of those who bought chairs also bought tables, what percent of customers bought tables? A. 60% B. 65% C. 70% D. 75% E. 80% Source: Veritas Prep | Difficulty: Hard

total number of people who bought table and chairs = a+b+c
according to question; (a+b) / (b+c) = 3:2 ........ 1)
Also, half of those who bought chairs also bought tables,(c+b)/2 = b

now one small point: why can’t (c+b)/2 = a+b (ie. half of those who bought chairs also bought tables)
if so then, 2(a+b) = c+b
BUT, 2(a+b) = 3(c+b) ..... as stated above

that would mean, c+b = 0 and this would make denominator in eqn 1) as 0 and this is not possible (The language of the question is a bit deceiving)

so we have to interpret "half of those who bought chairs also bought tables" as
(c+b)/2 = b
=> c = b = k (say)

then, putting it in equation 1:
2a+2k = 6k
a = 2k

now, % of people who bought tables = (a+b)/(a+b+c) * 100
=> 3k/4k * 100 = 75% people

Option D.
Re: Quant Question of the Day Chat [#permalink]
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