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While the GAMSAT Maths section does not exist in the real exam, Section 3 does have a few problems (particularly in GAMSAT Physics or GAMSAT Chemistry) that require basic mathematical skills or manipulations. Keep in mind that the GAMSAT March 2012 sitting was the first time ever that calculators were banned. Many students were surprised by the number of calculations they were required to perform on the real exam. So, is it possible to pass these GAMSAT Maths questions without the help of a calculator?
Well, if you are patient, you will learn that being efficient and using pattern recognition can be very powerful. You CAN actually make "magic" with numbers on the GAMSAT. Below are a few quick and useful tips and formulas to add to your GAMSAT Maths techniques.
*For advice on essential items to bring during the exam, please check out our forum on GAMSAT Test Day Items.
Have you seen these numbers on GAMSAT Physics or GAMSAT Chemistry exams: 1.44, 1.69? Do they ring a bell? You should have memorised all squares between 1 and 15. You likely have 1 to 10 stone cold! 11 squared is 121, 12 is 144, 13 is 169, 14 is 196, 15 is 225 . . . Test makers choose their numbers carefully. The moment you see 1.44 on the GAMSAT, there would be a high likelihood that taking the square root, which gives 1.2, would be required. Pattern recognition, yes?
Sometimes the GAMSAT will say, if B increases by 44%, by what % will A increase? Easy as pie! If B increases by 44%, that is the same as saying 1.44(B) and we know that root 1.44 is 1.2, which means the original sq root B = A has increased by 20%. (Of course, it's not a math test so they won't use "A" and "B" but rather they may present a physics equation to you). Even if they tell you, "given g = 9.8 m/s^{2}," you use 10 unless the answers are very close to each other.
Pi is 3.14, root 2 is 1.4, root 3 is 1.7. Don't be surprised if you need to calculate the perimeter (2 pi r) or area (pi r squared) of a circle. Be comfortable estimating the root of anything! Root 17? Well, the answer must be between 4 and 5 but closer to 4! Check the answers and don't calculate anything if there is only one answer that is between 4 and 4.5.
Fractions will usually permit you to be more efficient. For huge and tiny numbers, you need to be comfy with scientific notation. And if you can hang on to variables for as long as possible, that's even better. You may be surprised how many times mass m ends up being irrelevant as it happily cancels out!
Most past "gamsatters" felt that they rarely used their calculators for GAMSAT Maths. So relax! Be sure that you know the basics and work through all of ACER's practice materials without the use of a calculator and then math will not hold you back!
sin θ = opp/hyp 
cos θ = adj/hyp 
tan θ = opp/adj 
θ = sin^{1} x 
Estimate square root 3 as 1.7 and root 2 as 1.4 
r^{2} = x^{2} + y^{2} 
Equations of the type y = ax + b are known as linear equations since the graph of y (= the ordinate) versus x (= the abscissa) is a straight line. The value of y where the line intersects the y axis is called the intercept b. The constant a is the slope of the line. Given any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) on the line, we have:
y_{1} = ax_{1} + b
and
y_{2} = ax_{2} + b.
Subtracting the upper equation from the lower one and dividing through by x_{2}  x_{1} gives the value of the slope, a = (y_{2}  y_{1})/(x_{2}  x_{1}).
Note: a positive slope rises as it extends to the right (as in the graph below), a negative descends, and if the line is horizontal, then the slope is zero.
For any real number x, there exists a unique real number called the multiplicative inverse or reciprocal of x denoted 1/x or x^{1} such that x (1/x) = 1. The graph of the reciprocal 1/x for any x is:
There are classical curves which are represented or approximated iin the Gold Standard GAMSAT textbook as follows (if you do not have the book, we suggest doing a Google image search so you can identify these shapes of these graphs/curves): Sigmoidal curve (CHM 6.9.1, BIO 7.5.1), sinusoidal curve (PHY 7.1.1, 7.1.2), and hyperbolic curves (CHM 9.7 Fig III.A.9.3, BIO 1.1.2).
If you were to plot a set of experimental data, often one can draw a line (A.1.1) or curve (A.1.2/3, A.2.2) which can "best fit" the data. The preceding defines a regression line or curve. The main purpose of the regression graph is to predict what would likely occur outside of the experimental data.
a^{0} = 1
a^{1} = a
a^{n} a^{m} = a^{n+m}
a^{n}/a^{m} = a^{nm}
(a^{n})^{m} = a^{nm}
The exponential and logarithmic functions are inverse functions. That is, their graphs can be reflected about the y = x line.
Figure A.1: Exponential and Logarithmic Graphs. A > 0, A ≠ 1.
The rules of logarithms were discussed in context of Acids and Bases in General Chemistry (CHM 6.5.1). These rules also apply to the "natural logarithm" which is the logarithm to the base e, where "e" is an irrational constant approximately equal to 2.7182818. The natural logarithm is usually written as ln x or log_{e} x. In general, the power of logarithms is to reduce wideranging numbers to quantities with a far smaller range.
For example, the graphs commonly seen in the Gold Standard GAMSAT textbook, including the preceding one, are drawn to a unit or arithmetic scale. In other words, each unit on the x and y axes represents exactly one unit. This scale can be adjusted to accommodate rapidly changing curves. For example, in a unit scale the numbers 1 (= 100), 10 (= 10^{1}), 100 (= 10^{2}), and 1000 (= 10^{3}), are all far apart with varying intervals. Using a logarithmic scale, the sparse values suddenly become separated by one unit: Log 10^{0} = 0, log 10^{1} = 1, log 10^{2} = 2, log 10^{3} = 3, and so on.
In practice, logarithmic scales are often used to convert a rapidly changing curve (e.g. an exponential curve) to a straight line. It is called a semilog scale when either the abscissa or the ordinate is logarithmic. It is called a loglog scale when both the abscissa and the ordinate are logarithmic.
Many GAMSAT problems every year rely on a basic understanding of logarithms for pH problems, rate law (CHM 9.10) or a 'random' Nernst equation question (BIO 5 Appendix). Here are the rules you must know:
log_{a}a = 1
log_{a}M^{k} = k log_{a}M
log_{a}(MN) = log_{a}M + log_{a}N
log_{a}(M/N) = log_{a}M  log_{a}N
10^{l°g}_{10}^{M} = M
For example, let us calculate the pH of 0.001 M HCl. Since HCl is a strong acid, it will completely dissociate into H^{+} and Cl^{}, thus:
[H+] = 0.001
log[H^{+}] = log (0.001)
pH = log(10^{3})
pH = 3 log 10 (rule #2)
pH = 3 (rule #1, a = 10)
Algebraic expressions can be factored or simplified using standard formulae:
a(b + c) = ab + ac
(a + b)(a  b) = a^{2}  b^{2}
(a + b)(a + b) = (a + b)^{2} = a^{2} + 2ab + b^{2}
(a  b)(a  b) = (a  b)^{2} = a^{2}  2ab + b^{2}
(a + b)(c + d) = ac + ad + bc + bd
Positive + Positive = Positive
5 + 4 = 9
Negative + Negative = Negative
(6) + (2) = 8
Positive + Negative = Sign of the highest number and then subtract
(5) + 4 = 1
(8) + 10 = 2
Negative  Positive = Negative
(7)  10 = 17
Positive  Negative = Positive + Positive
= Positive
6  (4) = 6 + 4 = 10
Negative  Negative = Negative + Positive
= Sign of the highest number and then subtract
(8)  (7) = (8) + 7 = 1
Negative x Negative = Positive
(2) x (5) = 10
Positive/Positive = Positive
8/2 = 4
Negative x Positive = Negative
(9) x 3 = 27
Positive/Negative = Negative
64/(8) = 8
Here are some challenging math problems, but if you can apply the basic rules then real GAMSAT math (i.e. related to physics and general chemistry problems) will not give you difficulties. The questions are followed by answers and worked solutions/explanations.
x^{6}y^{3}
x^{5}y^{3}
x^{5}y^{2}
xy^{3}
0
16x^{5}
16x^{6}
16x^{8}
16x^{10}
16x^{12}
x^{2}  y^{2} + 9
x^{2} + y^{2} + 9
x^{2} + y^{2} + 2xy + 6x + 6y + 9
x^{2} + y^{2}  2xy + 6x  6y + 9
x^{2}  y^{2}  2xy + 6x  6y + 9
x^{a}
x^{ab}
x^{a + 2b}
x^{5a  2b}
x^{5a + 2b}
8
4
1
1/2
1/4
3
2
1
1/2
1/3
0
1
2
3
4
log_{b}(y^{xy})
log_{b}(y^{x+y})
log_{b}(y^{xy})
log_{b}(xy^{xy})
log_{b}(x^{y})
e
3
6
3e
9
1/4
1/2
1
2
4
y = 2^{x}  1
y = (2^{x})+ 1
y = 2^{x}
y = (2^{x})
y = (x^{2})
y = ln (x)
y = ln (x  1)
y = ln (x + 1)
y = ln (x  1)
y = ln (x + 1)
Decreases
Increases
Remains Constant
Sometimes Decreases, Sometimes Increases
Not Enough Information
Decreases
Increases
Remains Constant
Sometimes Decreases, Sometimes Increases
Not Enough Information
B
D
D
A
C
A
B
B
E
A
D
E
B
B
(x^{2})(y^{2})(x^{3})(y)(x^{0}) = (x^{2} x^{3} x^{0})(y^{2}y)
y^{2}y = (y)(y)(y) = y^{2+1} = y^{3}
(x^{2} x^{3} x^{0})(y^{2}y)
= x^{2+3+0}y^{2+1}
= x^{5}y^{3}
. (2x)^{2}
and (((2x^{2})^{3})^{2})
. First consider (2x)^{2}
. Because the exponent is negative, this is equal to the inverse of the positive power.(2x)^{2} = 1/(2x)^{2}
1/(2x)^{2} = 1/(2^{2}x^{2})
(((2x^{2})^{3})^{2})
. When you raise a power to another power, multiply the exponents together. And don't forget to distribute through the parenthetical expression.(((2x^{2})^{3})^{2}) = ((2^{3}x^{(2)}^{(3)})^{2}) = (2^{(3)}^{(2)}x^{(2)}^{(3)}^{(2)}) = 26x12
(2x)^{2}(((2x^{2})^{3})^{2})
= [1/(2^{2}x^{2})](2^{6}x^{12})
= (2^{6}x^{12})/(2^{2}x^{2})
= (2^{62}x^{122})
= 2^{4}x^{10}
= 16x^{10}
. (x  y + 3)^{2}
is really (x  y + 3)(x  y + 3)
, NOT (x^{2}  y^{2} + 3^{2})
. Now let's multiply and expand:(x  y + 3)(x  y + 3)
= x^{2}  xy + 3x  xy + y^{2} 3y + 3x  3y + 9
= x^{2} + y^{2}  2xy + 6x  6y + 9
. (x^{2a + b})(x^{a  2b}) / (x^{2a  b})
= (x^{2a+b+a2b}) / (x^{2a  b})
= (x^{3a  b}) / (x^{2a  b})
= (x^{3ab2a+b})
= x^{a}
. ((y^{2/3})^{1/2}) / (x^{1/2})
= (y^{1/3}) / (x^{1/2})
= (x^{1/2}) / (y^{1/3})
x=4
and y=8
. Notice that 4=2^{2}
and 8=2^{3}
.= (4^{1/2}) / (8^{1/3})
= (2^{(2)1/2}) / (2^{(3)1/3})
= 2^{1}/2^{1}
= 1
. log_{6}(24) + log_{6}(9)
= log_{6}(24*9)
= log_{6}(216)
= log_{6}(6^{3})
6
raised to what power is equal to 6^{3}
? The answer is, of course, 3
. log_{10}(70) = x + log_{10}(7)
log_{10}(70)  log_{10}(7) = x
log_{10}(70/7) = x
log_{10}(10) = x
1 = x
. x(log_{b}(y)) + y(log_{b}(y))
= log_{b}(y^{x}) + log_{b}(y^{y})
= log_{b}(y^{x}y^{y})
= log_{b}(y^{x+y})
. (e^{3})log_{3}(27) + ln (1)ln (e)
= ln (e^{3})log_{3}(27) + 0*1
= 3 log_{3}(27)
= 3(3)
= 9
. log_{b}(9)  2(log_{b}(12)) = 2
log_{b}(9)  log_{b}(12^{2}) = 2
log_{b}(9/144) = 2
log_{b}(1/16) = 2
b^{2} = 1/16
b = √(1/16)
b = ¼
. (0, 1)
. Plugging x = 0
into the given equations we can rule out all options except y = (2^{x})
, so that is the solution. (0, 0)
. Plugging in y = 0
to the given equations we can eliminate all but y = ln (x+1)
and y = ln (x+1)
. Next find the vertical asymptote. It appears to be located at x = 1
, and the curve approaches negative infinity. When x is small, ln (x+1)
is positive, so it cannot be the solution. Thus the graph represents y = ln (x+1)
. f(x) = 2^{x1}
does not change the behavior of the slope, it simply shifts the graph along the xaxis. The slope of f(x) = 2^{x}
increases exponentially as x increases.y = log_{10}(x)
, the logarithm graph reflected about the xaxis. So the slopes along the curve are the opposite of the positive logarithm graph. Therefore when we decrease the value of x (moving right to left along the axis) the slope increases. If you are unsure of your solution, plug in test points to check.Discuss any of our GAMSAT maths questions or worked solutions here: GAMSAT Math Forum.
Get 1 full hour access to free GAMSAT Physics and GAMSAT Chemistry and Biology videos online. Register here: Free GAMSATprep User Account.
Our Free GAMSAT Advice page contains links to various free resources that we believe can help increase your GAMSAT test performance. We have placed links that will help you be more analytical in the humanities and social sciences (Section 1) while, at the same time, helping you develop relevant content that you can use for your essays (Section 2). We have also placed links to officially corrected real past Writing Sample tests for the MCAT which simulates Writing Test A (argumentative) of GAMSAT Section 2 in terms of timing, length and format. For Section 3 advice, we have placed links to physics formulas (equation lists) and organic chemistry mechanisms which will help you practice for the real test. We have also recently added a few more helpful links to our list of free resources: monthly online seminar, free GAMSAT practice test and free Writing Test B essays with corrections/comments by our GS Essay Correction Service.
We believe that a student who has a long history of regularly reading books or editorials, writing essays at a high level and has a strong scientific intuitive reasoning may only do a few practice tests and then excel when sitting the real GAMSAT. Most students must prepare much more than that. In our estimation, adequate GAMSAT preparation requires, on average, 36 hours per day for 36 months depending on your past academic and life experiences. So we have created a way for you to build a free personal study schedule GAMSAT test preparation. The Gold Standard believes that with adequate time, practice and preparation that you can achieve the GAMSAT score that you want. Good luck!
Depending on where you live, add (especially the editorial sections):
Australia
Ireland
UK
For English as a Second Language (ESL) students: http://www.eslfast.com
Corrected Writing Samples (simulates GAMSAT Writing Test A):
These books are not free but very helpful for essay writing:
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Personal Study Schedule
Personal Notes: GAMSAT Study Tips
2020 GAMSAT Information Booklet from ACER
Questions, Comments, Concerns or Suggestions
If you have always been an avid reader of novels and newspapers, who picks up new information in class quickly (irrespective of your actual grades) and you have or are completing a science degree, you might be one of the rare students who study for 1  3 weeks  or not at all  and still end up with a great GAMSAT score!
For the great majority of students, an average study time or GAMSAT revision timetable would be 3 to 6 hours/day for 3 to 6 months. If you have absolutely no science background (not even in high school) then you might need a couple of more months to learn the basics. Whatever your background, be sure to spend at least half of your study time sitting and carefully reviewing practice exams (posttest analysis) covering all 3 GAMSAT sections.
Let's repeat that: STUDY and POSTTEST ANALYSIS. These make up your formula for a smart GAMSAT study schedule.
Here's a free GOLD STANDARD tool to help you design your own personal GAMSAT study schedule:
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The first step to an effective study preparation is to identify your strengths and weaknesses. Would Physics be your strongest, followed by Biology, then General Chemistry with Organic Chemistry and Humanities as the weakest? Do you even need some guidance in the Section 2 writing tasks?
Now remember that the basis of your assessment should be GAMSATspecific and there are three ways for you to find out:
Your GAMSAT revision timetable must include posttest analysis. Ideally, you would use worked solutions to review the explanations for each question, thoroughly understanding why you got certain answers wrong. For ACER's GAMSAT Sample Questions ('blue booklet'), GAMSAT Practice Questions ('red booklet'), Practice Test 1 ('green booklet'), Practice Test 2 ('purple booklet') and Practice Test 3 ('pink booklet'), Gold Standard has uploaded more than 20 hours of worked solutions to YouTube covering 500^{+} multiplechoice Section 3 questions, for free: Gold Standard GAMSAT YouTube Channel. However, before sitting fulllength practice GAMSAT tests, you should complete your content review so that you can use practice tests as trial runs. We have constructed an additional 10 fulllength simulated exams should you require the extra practice.
After assessing your strengths and weaknesses using the three methods described above, you may now rank the subjects according to how you deem each in terms of difficulty. You can then determine how often in a week you would need to study your weakest subject (ranked as number 1, i.e., your top priority) down to your strongest (ranked as number 5).
Our recommendation is that you study your most and second most difficult subjects, as well as your easiest subject, twice a week.
As to the number of hours per day that you need for revision, an average of 36 hours would be ideal. Nevertheless, this should be realistically determined relevant to your university classes and or working hours.
Your academic grades also spell a difference. GAMSAT prep can take as long as 4 to 6 months if you averaged a C or if you have not taken two or more of the science courses in the undergraduate level. Granting you have taken all science sections and averaged an A, three months or less may be all you need.
Momentum, Impulse PHY 4.3 
M = mv 

Energy (conservation) PHY 5.5 
E_{T} = E_{k} + E_{p} 

Work, Power PHY 5.7 
P = ΔW/Δt 

Current PHY 10.1 
I = Q/t 

Resistors (series, par.) PHY 10.2 
R_{eq} = R_{1} + R_{2} . . . 
1/ R_{eq} = 1/ R_{1} +1/ R_{2} . . . 
Capacitors (series, par.) PHY 10.4 
1/ C_{eq} = 1/ C_{1} +1/ C_{2} . . . 
C_{eq} = C_{1} + C_{2} . . . 
Kirchoff's Laws PHY 10.3.1 
Σi = 0 at a junction 
ΣΔV = 0 in a loop 
Torque forces PHY 4.1 
L_{1} = F_{1}× r_{1} (CCW + ve) 
L_{2} = F_{2} × r_{2} (CW ve) 
Torque force at EQ PHY 4.1 
ΣF_{x} = 0 and ΣF_{y} = 0 
ΣL = 0 
Force PHY 2.2 
F = ma 

Weight PHY 2.1 
W = mg 

Pressure PHY 6.1.2 
P = F/A 

Buoyant Force PHY 6.1.1 
ρ = mass / volume 
F_{b}= Vρg = mg 
Optics PHY 11.3 
M = magnification =  i/o 
F = K_{G} ( m_{1} m_{2} / r^{2} ) PHY 2.4 and 9.1.2 
F = k ( q_{1} q_{2} / r^{2} ) 

V = IR PHY 10.1 and 10.5 
P = IV 
Paired Use 
v_{av} = Δ d / Δ t PHY. 1.4.1 
a_{av} = Δ v / Δ t 
(avg vel, acc) 
v = λ f PHY 7.1.2 and 9.2.4 
E = hf 
(f = 1/T) 
E_{k} = 1/2 mv^{2} PHY 5.34 
E_{p} = mgh 
(kin, pot E) 
Translational motion PHY 1.6 and 2.5 
x = x_{o} + v_{o} t + 1/2at^{2}  (Vf)^{2} = (Vo)^{2} + 2ax 
V_{f} = V_{o} + at 
Uniform circular motion PHY 3.3 
F_{c} = ma_{c} = mv^{2} /r 
a_{c}= v^{2} /r 
Work, Power PHY 5.1 and 5.7 
W = F d cosθ 
P = ΔW/Δt 
Spring Force, Work PHY 7.2.1 
F = kx 
W = kx^{2} /2 
Refraction PHY 7.2.1 
(sin θ_{1} )/(sin θ_{2} ) = v_{1} /v_{2} = n_{2} /n_{1} = λ_{1} /λ_{2} 
n = c/v 
Pressure PHY 6.1.2 
Δ Ρ = ρgΔh 

Atomic Physics PHY 12.4 
If the number of halflifes n are known we can calculate the percentage of a pure radioactive sample left after undergoing decay since the fraction remaining = (1/2)^{n} 
Frictional force PHY 3.2 
f_{max} = μN 
μk < μs always 
Momentum, Impulse PHY 4.3 
I = F Δt = ΔM 

Electric Force PHY 9.1.2 
F = qE 

Optics PHY 11.5 
1/ i + 1/ o = 1/ f = 2/r = Power 

Specific Gravity PHY 6.1.1 
SG = ρ substance / ρ water 
ρ = 1 g/cm^{3} = 10^{3} kg/m^{3} (H_{2}O) 
Note: Specific gravity (SG) is equivalent to the fraction of the height of a buoyant object below the surface of the fluid. 
Fluids in Motion PHY 5.34 
Bernouilli's Equation 
Ρ + ρgh + 1/2 ρv^{2} = constant 
Solids, Temp Δ PHY 5.34 
Linear Expansion 
L = L_{o} (1 + αΔ T ) 
Area Expansion PHY 6.3 
A = A_{o}(1 + γΔ T ) 

β = 3 α PHY 6.3 
Volume Expansion 
V = V_{o}(1 + βΔ T ) 
Doppler Effect: when d is decreasing use + v_{o} and  v_{s} PHY 8.5.1 
f_{o} = f_{s} (V ± v_{o} )/( V ± v_{s}) 

d = the distance between the plates PHY 10.4 
V = Ed for a parallel plate capacitor 

RH rule PHY 9.2.3 
Laplace's Law 
dF = dq v(B sin α) = I dl(B sin α) 
W = 1/2 CV^{2} PHY 10.4 
Work in Electricity 
Potential Energy ( PE ) = W = 1/2 QV 
ΔG° = RTln K_{eq} CHM 9.10 
Gibbs Free Energy 
ΔG = ΔH  TΔS 
Continuity (fluids) PHY 6.1.3 
A v = const. 
ρAv = const. 
Sound PHY8.3.1 4 
dB = 10 log _{10} (I/I_{0} ) 
beats = Δ f 
Thermodynamics PHY 8.7 
Q = mc Δ T 

Root Mean Sq PHY 10.5 
I_{rms} = I_{max} / √2 

Energy (conservation) PHY 12.3 
E = mc^{2} 
sin θ = opp/hyp 
cos θ = adj/hyp 
tan θ =opp/adj 
θ = sin^{1} x 
arcsec θ = sec^{1}θ 
r^{2} = x^{2} + y^{2} 
Please note: ACER announced in 2011 that calculators will no longer be permitted for GAMSAT Section 3. Our updated list of GAMSAT Physics Topics can be found towards the bottom of this page.
The following GAMSAT Physics Topic list or syllabus is not meant to be exhaustive nor definitive. It is a guideline for topics that we cover for the GAMSAT preparation course during our live classes and in the videos that we have online or as DVDs.
TOPICS: The Atom, Nuclear Reactions, Radioactive Decay and HalfLife, Electricity vs. Gravity, Electric Circuits, Kirchhoff's Laws, Characteristics of Waves, Diffraction, Optics, Sound, Doppler Effect, Electromagnetism, Electromagnetic Spectrum, Reflection, Refraction, Thin Lens, Snell's Law, The Critical Angle, Force and Motion, Weight and Units, Friction, Applying Newton's Laws, Trigonometry, Projectile Motion, Work, Circular Motion, WorkEnergy Theorem, Energy and Entropy, Momentum, Law of Torques, Fluids, Fluids in Motion, Archimedes' Principle
Related Helpful Links
Key Points
R = alkyl 
Et = ethyl 
X = halide 
R^{} MgX^{+} = Grignard reagent 
R^{} Li^{+} = alkyl lithium 
Grignard reagents and alkyl lithiums are special agents since they can create new CC bonds (see ORG 1.6).
*Reduction = addition of hydrogen or subtraction of oxygen. Mild reducing agents add fewer hydrogens/subtract fewer oxygens. Strong reducing agents add more hydrogens/subtract more oxygens. Crossreferencing to The Gold Standard GAMSAT textbook are found below.
Most reactions presented can be derived from basic principles (i.e. ORG 1.6, 7. 1). Many of the reactions are crossrefèrenced for further information.
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