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Quant Question of the Day Chat

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mysterymanrog
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Re: Quant Question of the Day Chat [#permalink] New post   15 Dec 2022, 08:06
gmatophobia wrote:
PS Question 1 - Dec 15 If x and y are positive integers and x^y=y^x+1, which of the following must be odd? A. xy B. x + y - 1 C. x + 2y D. 3x - y E. xy + 2 Source: GMAT Club Tests | Difficulty : Medium

x^y-y^x=1
Therefore, either (even-odd) or (odd-even). This implies that one of X or Y is even, and the other odd.
A) Out
B) (even)+(odd)=odd-1=even out
C) if x is even, even+even is even, out
D) either even-odd, or odd-even. Both are always odd.
E) even+even is even. Out.
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gmatophobia
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Re: Quant Question of the Day Chat [#permalink] New post   15 Dec 2022, 23:01
gmatophobia wrote:
DS Question 1 - Dec 15 Whenever martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2times the tens digit of the amount of his bill.If the amount of the Martin’s most recent restaurant bill was between $10 and $99, was the tip calculated by the martin on this bill greater than 15 percent of the amount of the bill? (1) The amount of the bill was between $15 and $50 (2) The tip calculated by the martin was $8 Source: Official Guide | Difficulty : Medium

Show SpoilerOA
B


gmatophobia wrote:
PS Question 1 - Dec 15 If x and y are positive integers and x^y=y^x+1, which of the following must be odd? A. xy B. x + y - 1 C. x + 2y D. 3x - y E. xy + 2 Source: GMAT Club Tests | Difficulty : Medium

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D
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Elite097
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Re: Quant Question of the Day Chat [#permalink] New post   15 Dec 2022, 23:27
Where all you practicing quant from ?
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gmatophobia
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Re: Quant Question of the Day Chat [#permalink] New post   15 Dec 2022, 23:39
Elite097 wrote:
Where all you practicing quant from ?


You can start with official questions, followed by questions from other sources.

Here are links to the 1000 series for DS and PS -
Complete 1000 Problem Solving Series
Complete 1000 Data Sufficiency Series
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gmatophobia
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Re: Quant Question of the Day Chat [#permalink] New post   15 Dec 2022, 23:56
DS Question 1 - Dec 16

If m and n are positive integers, is the remainder of (10^m + n)/3 larger than the remainder of (10^n + m)/3 ?

(1) m > n
(2) The remainder of n/3 is 2

Source: GMAT Club Tests | Difficulty: Hard
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gmatophobia
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Re: Quant Question of the Day Chat [#permalink] New post   16 Dec 2022, 00:38
PS Question 1 - Dec 16

What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24?

A) -5
B) -3
C) -2
D) 2
E) 5

Source: GMATPrepNow | Difficulty: Hard
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Re: Quant Question of the Day Chat [#permalink] New post   16 Dec 2022, 01:28
gmatophobia wrote:
PS Question 1 - Dec 16 What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24? A) -5 B) -3 C) -2 D) 2 E) 5 Source: GMATPrepNow | Difficulty: Hard

Case 1:

-x^2+4x-4=x^2+10x-24
-2x^2-6x+20=0
x^2+3x-10=0
(x+5)(x-2)=0

We need to check the solutions.
x^2+10x-24=0
(x+12)(x-2)
RHS is pos for solutions x2.
Because LHS is abs (which is always >=0) x=-5 is not within the pos range of RHS, so we can eliminate it.
X=2 is just the root of RHS and LHS, so it is fine.

Case 2:
x^2-4x+4=x^2+10x-24
-14x=-28
x=2

Once again, x=2.

Solution set is just 2, so the sum of all solutions is just 2. D
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Re: Quant Question of the Day Chat [#permalink] New post   16 Dec 2022, 03:45
DS Question 2 - Dec 16

A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

Source: Official Guide | Difficulty: Hard
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Re: Quant Question of the Day Chat [#permalink] New post   16 Dec 2022, 03:50
gmatophobia wrote:
DS Question 2 - Dec 16 A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department? (1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. (2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads. Source: Official Guide | Difficulty: Hard

1) Clearly INS.
2) 18,27,36.
We can have a case of 1 employee, which got 18 pens, 27 pencils, 36 pads, or 9 employees who got 2 pens 3 pencils and 4 pads each. INS.
3) No new info.
E.
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 16 Dec 2022, 08:56
gmatophobia wrote:
DS Question 1 - Dec 16 If m and n are positive integers, is the remainder of (10^m + n)/3 larger than the remainder of (10^n + m)/3 ? (1) m > n (2) The remainder of n/3 is 2 Source: GMAT Club Tests | Difficulty: Hard

E
it boils down to whether m+1 is divisible by 3 and whether n+1 is divisible by 3
B seems correct but m+1 still might be divisible by 3 and remainder would be 0 so we cannot say it’ll be greater for sure

mysterymanrog wrote:
Case 1: -x^2+4x-4=x^2+10x-24 -2x^2-6x+20=0 x^2+3x-10=0 (x+5)(x-2)=0 We need to check the solutions. x^2+10x-24=0 (x+12)(x-2) RHS is pos for solutions x2. Because LHS is abs (which is always >=0) x=-5 is not within the pos range of RHS, so we can eliminate it. X=2 is just the root of RHS and LHS, so it is fine. Case 2: x^2-4x+4=x^2+10x-24 -14x=-28 x=2 Once again, x=2. Solution set is just 2, so the sum of all solutions is just 2. D

actually LHS is a perfect square, (x-2)^2, so we can remove the modulus directly and solve that x=2 is the only solution

Originally posted by deferred2023 on 16 Dec 2022, 08:53.
Last edited by deferred2023 on 16 Dec 2022, 08:56, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 17 Dec 2022, 02:00
gmatophobia wrote:
PS Question 1 - Dec 16 What is the sum of all solutions to the equation |x² – 4x + 4| = x² + 10x – 24? A) -5 B) -3 C) -2 D) 2 E) 5 Source: GMATPrepNow | Difficulty: Hard

Show SpoilerOA
D


gmatophobia wrote:
DS Question 2 - Dec 16 A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department? (1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. (2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads. Source: Official Guide | Difficulty: Hard

Show SpoilerOA
E


gmatophobia wrote:
DS Question 1 - Dec 16 If m and n are positive integers, is the remainder of (10^m + n)/3 larger than the remainder of (10^n + m)/3 ? (1) m > n (2) The remainder of n/3 is 2 Source: GMAT Club Tests | Difficulty: Hard

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B


PS Question 1 - Dec 17

For an odd integer n, the function f(n) is defined as the product of all odd integers from 1 to n. The lowest odd prime factor f(71)-­1 lies between…

A. 3 and 10
B. 11 and 30
C. 31 and 50
D. 51 and 70
E. 71 and above

Source: Experts Global | Difficulty: Hard

DS Question 1 - Dec 17

Is the standard deviation of the numbers in list R less than the standard deviation of the numbers in list S ?

(1) The range of the numbers in R is less than the range of the numbers in S.
(2) Each number in R occurs once and each number in S is repeated.

Source: Official Guide | Difficulty: Hard

Originally posted by gmatophobia on 17 Dec 2022, 01:53.
Last edited by gmatophobia on 17 Dec 2022, 02:00, edited 3 times in total.
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Re: Quant Question of the Day Chat [#permalink] New post   17 Dec 2022, 02:10
gmatophobia wrote:
DS Question 1 - Dec 17 Is the standard deviation of the numbers in list R less than the standard deviation of the numbers in list S ? (1) The range of the numbers in R is less than the range of the numbers in S. (2) Each number in R occurs once and each number in S is repeated. Source: Official Guide | Difficulty: Hard

Should be E.

1) Clearly INS
2) Even if each number in R occurs once, we can have say (1)=R, and (2,2,99,99)=S, in which case S>R, or (1,6)=R (2,2,2,2)=S, in which case R>S.
INS.

3) no new info by combining these two statements.
E.
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Re: Quant Question of the Day Chat [#permalink] New post   17 Dec 2022, 06:55
PS Question 2 - Dec 17

The function f is defined for each positive three-digit integer n by f(n)=2^x * 3^y * 5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9∗f(v) , then m−v= ?

(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

Source: Official Guide | Difficulty : Medium
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Re: Quant Question of the Day Chat [#permalink] New post   17 Dec 2022, 10:04
gmatophobia wrote:
PS Question 2 - Dec 17 The function f is defined for each positive three-digit integer n by f(n)=2^x * 3^y * 5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9∗f(v) , then m−v= ? (A) 8 (B) 9 (C) 18 (D) 20 (E) 80 Source: Official Guide | Difficulty : Medium

I’m pretty sure the answer is D.

Taking f(m)=9*f(v)
2^a*3^b*5^c=9(2^x*3^y*5^z)
2^a-x*3^b-y*5^c-z=9
Since 3^2=9, a-x=0, b-y=2, c-z=0

which means the hundreds and ones digits are the same and the tena digits have a difference of 2 which means the difference is 20
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 17 Dec 2022, 23:08
gmatophobia wrote:
PS Question 1 - Dec 17 For an odd integer n, the function f(n) is defined as the product of all odd integers from 1 to n. The lowest odd prime factor f(71)-­1 lies between… A. 3 and 10 B. 11 and 30 C. 31 and 50 D. 51 and 70 E. 71 and above Source: Experts Global | Difficulty: Hard

Show SpoilerOA
E


gmatophobia wrote:
DS Question 1 - Dec 17 Is the standard deviation of the numbers in list R less than the standard deviation of the numbers in list S ? (1) The range of the numbers in R is less than the range of the numbers in S. (2) Each number in R occurs once and each number in S is repeated. Source: Official Guide | Difficulty: Hard

Show SpoilerOA
E


gmatophobia wrote:
PS Question 2 - Dec 17 The function f is defined for each positive three-digit integer n by f(n)=2^x * 3^y * 5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9∗f(v) , then m−v= ? (A) 8 (B) 9 (C) 18 (D) 20 (E) 80 Source: Official Guide | Difficulty : Medium

Show SpoilerOA
D

Originally posted by gmatophobia on 17 Dec 2022, 23:07.
Last edited by gmatophobia on 17 Dec 2022, 23:08, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink] New post   18 Dec 2022, 00:35
DS Question 1 - Dec 18

What is the value of m?

(1) |1 - x| = m - 3
(2) |2 - m| = 7.

Source: Experts Global | Difficulty : Medium

PS Question 1 - Dec 18

The last digit of 12^(12) + 13^(13) – 14^(14) * 15^(15) =

A. 0
B. 1
C. 5
D. 8
E. 9

Source: Veritas Prep | Difficulty : Hard
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 18 Dec 2022, 03:56
gmatophobia wrote:
DS Question 1 - Dec 18 What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7. Source: Experts Global | Difficulty : Medium

1) Clearly ins
2) Solve inequalitiy, m=-5 or 9.
3) ABS cannot be negative, m is 9.

C

gmatophobia wrote:
PS Question 1 - Dec 18 The last digit of 12^(12) + 13^(13) – 14^(14) * 15^(15) = A. 0 B. 1 C. 5 D. 8 E. 9 Source: Veritas Prep | Difficulty : Hard

B

12^12 has units digit of 6, 3^13 units digit of 3, 14^14 has units digit of 6, 15^5 has unit digit 5.
9-30=-21
units digit of 1

Originally posted by mysterymanrog on 18 Dec 2022, 03:54.
Last edited by mysterymanrog on 18 Dec 2022, 03:56, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink] New post   18 Dec 2022, 06:21
DS Question 2 - Dec 18

In the xy-plane, does the line y = 2x - 1 contain the point (p,q)?

(1) (2p - 1 - q)(3p + 7 - q) = 0
(2) (5p + 2 - q)(1 - 2p + q) = 0

Source: Experts Global | Difficulty : Hard
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 18 Dec 2022, 23:52
gmatophobia wrote:
DS Question 1 - Dec 18 What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7. Source: Experts Global | Difficulty : Medium

Show SpoilerOA
C


gmatophobia wrote:
PS Question 1 - Dec 18 The last digit of 12^(12) + 13^(13) – 14^(14) * 15^(15) = A. 0 B. 1 C. 5 D. 8 E. 9 Source: Veritas Prep | Difficulty : Hard

Show SpoilerOA
B


gmatophobia wrote:
DS Question 2 - Dec 18 In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? (1) (2p - 1 - q)(3p + 7 - q) = 0 (2) (5p + 2 - q)(1 - 2p + q) = 0 Source: Experts Global | Difficulty : Hard

Show SpoilerOA
E

Originally posted by gmatophobia on 18 Dec 2022, 23:51.
Last edited by gmatophobia on 18 Dec 2022, 23:52, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink] New post   Updated on: 19 Dec 2022, 00:35
gmatophobia wrote:
DS Question 2 - Dec 18 In the xy-plane, does the line y = 2x - 1 contain the point (p,q)? (1) (2p - 1 - q)(3p + 7 - q) = 0 (2) (5p + 2 - q)(1 - 2p + q) = 0 Source: Experts Global | Difficulty : Hard

Rephrase the question as
q=2p-1

1) We have two solutions

q=2p-1 or q=3p+7. NS
2) 5p+2=q, q=-2p+1.
NS.
3) Combing both we still cannot determine. E.

Originally posted by mysterymanrog on 19 Dec 2022, 00:34.
Last edited by mysterymanrog on 19 Dec 2022, 00:35, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
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