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Practice Questions Chat 07 Jan 2023, 14:25
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gmatophobia
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
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Answer should be C. 40*30+pi*20^2-pi*10^2 =>1200+400pi-100pi =>1200+300pi
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Practice Questions Chat 07 Jan 2023, 15:11
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gmatophobia
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
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We want to separate the figure into 3 sections: the 30x40 rectangle, the shaded semicircle and the non-shaded semi.
The area of the rectangle is simple: 30x40 is just 1200
We are given the radius of the shaded semicircle, so its area is just 100pi/2
We are also given the radius of the big semicircle, so its area is just 400pi/2
Because we want to exclude the shaded region, we need to subtract the shaded semicricle area from the big semicircle. So 400pi/2-100pi/2=300pi/2=150pi

The total area of the parking lot is then, 1200+150pi.

E is the clear answer.
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Practice Questions Chat 08 Jan 2023, 00:18
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gmatophobia
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
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one doubt :
since the question doesn’t mention integer nature of m or n,
can we treat floating point numbers or fractions (e.g.- 2.4, 31.45 etc.) as even / odd numbers ?

gmatophobia
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
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total area asked is :
area of rectangle + area of driveway
= 40*30 + (1/2 *(pi)*(20^2 - 10^2))
= 1200 + 150(pi)
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one doubt : since the question doesn’t mention integer nature of m or n, can we treat floating point numbers or fractions (e.g.- 2.4, 31.45 etc.) as even / odd numbers ?
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Whenever we use the term even / odd, it refers to integers.
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Practice Questions Chat Updated on: 08 Jan 2023, 00:33
Originally posted by AbhinavKumar on 08 Jan 2023, 00:32.
Last edited by AbhinavKumar on 08 Jan 2023, 00:33, edited 1 time in total.
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then going by definition that odd/even refers to integers only.

statement 1:
is sufficient as we know individual nature of m and n, combined with the fact
that powers don’t destroy even/odd nature of number.

statement2:
m-n is odd.
eg1-
45.5 - 20.5 = 25 odd
now, 45.5 + (20.5)^3 = not an integer, neither yes nor no as answer.

eg2 -
4 - 1 = 3 odd
4 + 1^3 = 5 odd (we get yes as answer)
we get not a definite answer, so statement 2 not suff.


Option A ?

I hope this is the right way!
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Practice Questions Chat Updated on: 08 Jan 2023, 00:42
Originally posted by gmatophobia on 08 Jan 2023, 00:35.
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then going by definition that odd/even refers to integers only. statement 1: is sufficient as we know individual nature of m and n, combined with the fact that powers don’t destroy even/odd nature of number. statement2: m-n is odd. eg1- 45.5 - 20.5 = 25 odd now, 45.5 + (20.5)^3 = not an integer, neither yes nor no as answer. eg2 - 4 - 1 = 3 odd 4 + 1^3 = 5 odd (we get yes as answer) we get not a definite answer, so statement 2 not suff. Option A ?
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Yep ! A is the correct answer :thumbsup:

gmatophobia
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
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A

gmatophobia
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
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E

DS Question 1 - Jan 08

Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf?

(1) The 8 thinnest books each have a thickness of 2 inches.

(2) The 2 thickest books each have a thickness of 5 inches.

Source: Kaplan | Difficulty: Hard
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Practice Questions Chat 08 Jan 2023, 01:17
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gmatophobia
DS Question 1 - Jan 08 Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf? (1) The 8 thinnest books each have a thickness of 2 inches. (2) The 2 thickest books each have a thickness of 5 inches. Source: Kaplan | Difficulty: Hard
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total width of shelf = 5ft = 60in
total books = 22,
we need the maximize number of books that go on the shelf

statement1:
8 thinnest book with 2 in thickness covers 16in
but how many more books can go on remaining length of shelf?
we may never know as we don’t have thickness of rest of the books
so, not a sufficient statement

statement 2:
thickest books have 5in width
there are 2 of them,

all books can go on 5.5ft = 66in of shelf (as given in question stem)
if 1st thickest book is removed, we are left with 61 inch space
if 2nd thickest book is removed, we are left with 56 inch space

therefore, remaining 20 books can go onto 5ft (60in) book shelf.
As, rest assured remaining 20 books have less than 5in thickness

Option B ?
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Practice Questions Chat 09 Jan 2023, 00:21
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gmatophobia
DS Question 1 - Jan 08 Susan has a 5-foot long bookshelf that she wants to fill with 22 books of differing sizes. Each book can fit on the shelf, but they cannot all fit on the shelf. In order to fit all of her books on the same shelf, she would need a 5.5-foot long bookshelf. What is the maximum number of books she can fit on her shelf? (1) The 8 thinnest books each have a thickness of 2 inches. (2) The 2 thickest books each have a thickness of 5 inches. Source: Kaplan | Difficulty: Hard
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B

PS Question 1 - Jan 09

What is the volume of the largest cube that can fit inside a cylinder with radius 2 and height 3?

A) 9
B) 8√2
C) 16
D) 16√2
E) 27

Source: GMATPrepNow | Difficulty: Hard
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Practice Questions Chat 09 Jan 2023, 06:46
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DS Question 1 - Jan 09

If X=P∗(N^K)+P where P, N and K are positive integers, is X divisible by 2?

(1) N + KN = 915
(2) P^35+35^P is Even

Source: Math Revolution | Difficulty: Medium
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Practice Questions Chat Updated on: 09 Jan 2023, 07:02
Originally posted by AbhinavKumar on 09 Jan 2023, 06:53.
Last edited by AbhinavKumar on 09 Jan 2023, 07:02, edited 1 time in total.
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gmatophobia
PS Question 1 - Jan 09 What is the volume of the largest cube that can fit inside a cylinder with radius 2 and height 3? A) 9 B) 8√2 C) 16 D) 16√2 E) 27 Source: GMATPrepNow | Difficulty: Hard
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the size of cube depends on the size of opening of the cylinder.
so, given the 2cm radius of cylinder,
the square that it can hold has side as 2*root(2)units
hence vol. of cube is 16*root(2)
option D

gmatophobia
DS Question 1 - Jan 09 If X=P∗(N^K)+P where P, N and K are positive integers, is X divisible by 2? (1) N + KN = 915 (2) P^35+35^P is Even Source: Math Revolution | Difficulty: Medium
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question stem: is x even?

statement1:
N(K+1)=915=5*3*61

N can be any of those odd integers, power of k is not going to affect odd/even nature
in original expression X = P(N^K+1)
N^K+1 term will be even so x is even
Stetement 1 is suff


statement2:
P^35 + ODD = EVEN
P is ODD

what about N, no info is given
insufficient


option A?
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Yes statement 1 is sufficient.
Factors of 915 are 5*3*61
ACC to statement 1: N+KN =915
WE CAN WRITE IT AS N (1+K) = 915
So N must be a odd number ( either 3,5, or 61 or a product of any two of them) and the 1+K term must also be odd, which means that K must be even.
So when we know that N is odd and K is even, take example of 3 and 2 in the question statement. Answer will always be even. Statement 1 is sufficient.

Statement 2 We don’t know anything about N. Can be odd or even. You can experiment with one odd and one even number to test it out. Answer is inconsistent. Statement 2 is not sufficient.
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Practice Questions Chat Updated on: 09 Jan 2023, 23:18
Originally posted by gmatophobia on 09 Jan 2023, 23:15.
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DS Question 1 - Dec 10

P, Q, R, S, and T represent five distinct points on the circumference of a circle. Is arc PQR longer than arc RST?

(1) Chord QT is longer than chord QS.
(2) Chord ST is longer than chord PT

Source: Princeton Review | Difficulty: Hard

PS Question 1 - Dec 10

If y=|x+5|−|x−5|, then y can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Source: GMAT Club Tests | Difficulty: Hard
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Practice Questions Chat Updated on: 11 Jan 2023, 00:27
Originally posted by gmatophobia on 11 Jan 2023, 00:17.
Last edited by gmatophobia on 11 Jan 2023, 00:27, edited 2 times in total.
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gmatophobia
DS Question 1 - Dec 10 P, Q, R, S, and T represent five distinct points on the circumference of a circle. Is arc PQR longer than arc RST? (1) Chord QT is longer than chord QS. (2) Chord ST is longer than chord PT Source: Princeton Review | Difficulty: Hard
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gmatophobia
PS Question 1 - Dec 10 If y=|x+5|−|x−5|, then y can take how many integer values? A. 5 B. 10 C. 11 D. 20 E. 21 Source: GMAT Club Tests | Difficulty: Hard
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E

DS Question 1 - Jan 11

A rectangular tank of dimensions 35 inches, 16 inches and ’X’ inches respectively is completely filled with water. All its water is emptied into a cylindrical tank of radius 14 inches. What is the height of the cylindrical tank?

(1) X = 11

(2) Rectangular tank has a volume of 6160 cubic inches

Source: Others | Difficulty: Hard Tricky
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Practice Questions Chat 11 Jan 2023, 06:49
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gmatophobia
DS Question 1 - Jan 11 A rectangular tank of dimensions 35 inches, 16 inches and ’X’ inches respectively is completely filled with water. All its water is emptied into a cylindrical tank of radius 14 inches. What is the height of the cylindrical tank? (1) X = 11 (2) Rectangular tank has a volume of 6160 cubic inches Source: Others | Difficulty: Hard Tricky
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The question is playing with meaning of question stem ,that’s why it seems to have been marked as "tricky"

even if we "empty" the rectangular tank into the cylindrical tank, we don’t know if the
later tank is filled upto the brim. We can’t find the actual height of cylindrical tank,
but all we can find is the height till where that tank got filled up.

Hence going with option E
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Practice Questions Chat 11 Jan 2023, 10:09
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gmatophobia
DS Question 1 - Jan 11 A rectangular tank of dimensions 35 inches, 16 inches and ’X’ inches respectively is completely filled with water. All its water is emptied into a cylindrical tank of radius 14 inches. What is the height of the cylindrical tank? (1) X = 11 (2) Rectangular tank has a volume of 6160 cubic inches Source: Others | Difficulty: Hard Tricky
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Great question - nearly got trapped.
The key to this is to understand that we are not given any information of the volume of the tank. Even if the water is poured in from the cube, we do not know if the water overfills the tank, if it fills it exact, partially, etc.

Notice that in this question, both statement 1 and 2 give the exact same information. This means that the answers can only be D or E. So, even if you don’t see the logic, It’s still a 50/50 question from a random guess :p
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It will be "too easy" to go with D though because both statements are surprisingly pointing to same inference which is the value of x. BUT we don’t know if the cylindrical tank will be "fully filled up to the brim" once rectangular tank is emptied into cylindrical tank, given the fact both statement doesn’t even touch this point, I would bet my money on option E ;)
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Practice Questions Chat Updated on: 13 Jan 2023, 04:21
Originally posted by gmatophobia on 13 Jan 2023, 04:20.
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DS Question 1 - Jan 13

If n is a positive integer, is n^3 - n divisible by 24?

(1) n is divisible by 6
(2) n = 8m + 4, where m is an integer

Source: 800 Score | Difficulty: Hard
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gmatophobia
DS Question 1 - Jan 13 If n is a positive integer, is n^3 - n divisible by 24? (1) n is divisible by 6 (2) n = 8m + 4, where m is an integer Source: 800 Score | Difficulty: Hard
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Rewrite n^3-n as (n-1)(n)(n+1)

Now this is always divisible by 6, so to be divisible by 24 it has to have 2 more twos.

1) n=m6

if n=6, 5*6*7 is not divisible.
if n=24 it is divisible. Ins.

2) n=8m+4
n=4,12,20,28, 36, 44 etc

if n=12, 11*12*13 is not m24
if n=4, 3*4*5 is clearly not
if n=20 19*20*21 is clearly not.
if n=28, 27*28*29 is clearly not divisible by 24.

I will conclude B, although there are probably far better ways to solve this.
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gmatophobia
DS Question 1 - Jan 13 If n is a positive integer, is n^3 - n divisible by 24? (1) n is divisible by 6 (2) n = 8m + 4, where m is an integer Source: 800 Score | Difficulty: Hard
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Going by the same approach as mentioned above by mysterymanrog. Seems like Option B it is.
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Practice Questions Chat Updated on: 14 Jan 2023, 00:42
Originally posted by gmatophobia on 14 Jan 2023, 00:32.
Last edited by gmatophobia on 14 Jan 2023, 00:42, edited 1 time in total.
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Rewrite n^3-n as (n-1)(n)(n+1) Now this is always divisible by 6, so to be divisible by 24 it has to have 2 more twos. 1) n=m6 if n=6, 5*6*7 is not divisible. if n=24 it is divisible. Ins. 2) n=8m+4 n=4,12,20,28, 36, 44 etc if n=12, 11*12*13 is not m24 if n=4, 3*4*5 is clearly not if n=20 19*20*21 is clearly not. if n=28, 27*28*29 is clearly not divisible by 24. I will conclude B, although there are probably far better ways to solve this.
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Nice approach - Here is my take on the question

Ques: Is n^3 - n divisible by 24

n(n+1)(n-1) divisible by (2^3 * 3)

In other words, does the product n(n+1)(n-1) contains at least 3 two(s) and 1 three(s)

Statement 1 is quite straight forward

Statement 2

n = 8m + 4

n = 4(2m+1)

n = 4 * odd = 2^2 * odd

We know that n contains ONLY 2 two(s). The odd factor of n will not contribute any two nor will n+1 or n-1 contribute the third two (as both of n+1 and n-1 are odd)

In other words, IMO we can avoid testing cases.

Kudos to both for solving !

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
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